## A Brief Overview Of Slope And Its Units

Aidan Philbin

Slope, or m as we often write it in equations, describes the way a function changes. The slope of a function y is the change in y divided by the change in x:

m = y/x

Linear graphs are graphs of straight lines, and can be defined by their slope, m, and their y-intercept, b:

y = m*x + b

In the figure below, there is a linear function plotted on a graph. If we want to find the slope of this function, we must choose two points on the line, and use Equation . Lets use and . We will have:

m = ya/xa = / = 3/6=1/2

Because this function is linear, we find the same slope using any two points, as shown below.

Alright so we know how to interpret the slope of a line as its rate of change, but what would the units of slope be? Lets work trough a word problem to sort it out.

A runner runs for different time intervals, and records how far they run each time. They produce the scatter plot below, and fit a line to it to find the slope. What exactly are they finding? What are the units?

So if theyre calculating slope, theyre using Equation : m = y/x. Looking at the plot, the y-axis has units of distance and the x-axis has units of time, so m = y/x = distance/time. We recognize distance/time as velocity. Because this is a line of best fit, the slope is the average velocity of the runner. So for the units, in this plot slope has units of meters/second.

Generally:

units of slope=/

## What Does A Positive Slope Mean In A Position Vs Time Graph

velocityThe principle is that the slope of the line on a position-time graph reveals useful information about the velocity of the object. If the velocity is changing, then the slope is changing . If the velocity is positive, then the slope is positive .

## Is C The Y Intercept

One form of the equation of a straight line is called the slope-intercept form because it contains information about these two properties. The value of c is called the vertical intercept of the line. It is **the value of y when x = 0**. When drawing a line, c gives the position where the line cuts the vertical axis.

**Don’t Miss: Draw The Lewis Structure For Ccl4. **

## Slopes And General Relationships

First note that graphs in this text have perpendicular axes, one horizontal and the other vertical. When two physical quantities are plotted against one another in such a graph, the horizontal axis is usually considered to be an * independent variable* and the vertical axis a * dependent variable*. If we call the horizontal axis the *x*-axis and the vertical axis the *y*-axis, as in Figure 1, a straight-line graph has the general form

Here *m* is the * slope*, defined to be the rise divided by the run of the straight line. The letter *b* is used for the * y-intercept*, which is the point at which the line crosses the vertical axis.

Figure 1. A straight-line graph. The equation for a straight line is .

## What Does Slope Mean In Real Life

Slope is **a measure of steepness**. Some real life examples of slope include: in building roads one must figure out how steep the road will be. skiers/snowboarders need to consider the slopes of hills in order to judge the dangers, speeds, etc. when constructing wheelchair ramps, slope is a major consideration.

**Also Check: Cpm Algebra 1 Chapter 9 Answers Pdf **

## What Is The Purpose Of Slope

Slope measures the rate of change in the dependent variable as the independent variable changes. Mathematicians and economists often use the Greek capital letter D or D as the symbol for change. Slope shows the change in y or the change on the vertical axis versus the change in x or the change on the horizontal axis.

## Graphs Of Motion Where Acceleration Is Not Constant

Now consider the motion of the jet car as it goes from 165 m/s to its top velocity of 250 m/s, graphed in Figure 6. Time again starts at zero, and the initial displacement and velocity are 2900 m and 165 m/s, respectively. Acceleration gradually decreases from 5.0 m/s2 to zero when the car hits 250 m/s. The slope of the *x* vs. *t* graph increases until *t*=55 s, after which time the slope is constant. Similarly, velocity increases until 55 s and then becomes constant, since acceleration decreases to zero at 55 s and remains zero afterward.

Figure 6. Graphs of motion of a jet-powered car as it reaches its top velocity. This motion begins where the motion in Figure 3 ends. The slope of this graph is velocity it is plotted in the next graph. The velocity gradually approaches its top value. The slope of this graph is acceleration it is plotted in the final graph. Acceleration gradually declines to zero when velocity becomes constant.

**Recommended Reading: Ccl4 Electron Geometry **

## The Slopes Of These Graphs Represent What

- 6

- 0

- 35,797

- 12,516

For one of them, I am asked to plot the current vs the magnetic field .The slope is supposed to give me a value, I have the slope, no clue what the value would represent. After some research I found that people are saying it represents the loops?No clue what that is.

Anyway I also have to plot the distance vs the magnetic field strength and the slope is supposed to be the permeability of a vacuum. I get 2E-7. Using 4piE-7, that’s a deviation of 85%. I do have a feeling something is not right here.

## Example 3 Calculating Acceleration From A Graph Of Velocity Versus Time

Calculate the acceleration of the jet car at a time of 25 s by finding the slope of the *v* vs. *t* graph in Figure 6.

**Strategy**

The slope of the curve at *t *= 25 s is equal to the slope of the line tangent at that point, as illustrated in Figure 6.

**Solution**

Determine endpoints of the tangent line from the figure, and then plug them into the equation to solve for slope, *a*.

**Discussion**

Note that this value for *a* is consistent with the value plotted in Figure 6 at *t *= 25 s.

A graph of displacement versus time can be used to generate a graph of velocity versus time, and a graph of velocity versus time can be used to generate a graph of acceleration versus time. We do this by finding the slope of the graphs at every point. If the graph is linear , it is easy to find the slope at any point and you have the slope for every point. Graphical analysis of motion can be used to describe both specific and general characteristics of kinematics. Graphs can also be used for other topics in physics. An important aspect of exploring physical relationships is to graph them and look for underlying relationships.

**Also Check: Slader Holt Geometry **

## What Does The Constant C Represent

In the paper of 1856 Webers constant was introduced with these words and the constant c represents that **relative speed, that the electrical masses e and e must have and keep, if they are not to affect each other**. So it appears that c originated as a letter standing for constant rather than celeritas.

## Area Under The Acceleration Graph

The area under the acceleration graph represents the change in velocity. In other words, the area under the graph for a certain time interval is equal to the change in velocity during that time interval.\Let us consider the below example to understand better:

The graph below shows a constant acceleration of 4 m/s2 for a time of 9 s.

Acceleration is defined as,

We can find the change in velocity by finding the area under the acceleration graph.

Substituting the values, we get

This calculation gave us the change in velocity during the given time interval. To calculate the final velocity, we need to use the definition of change in velocity.

Substituting the values in the equation, we get

Therefore, the final velocity of the racer is 44 m/s.

**Watch the video and learn the velocity-time graph and displacement-time graph in detail. By the end of this video, you will learn what do the slope of the displacement-time graph and velocity-time graph signify.**

**You May Like: Shape Of Sf5+ **

## Is C The Y

With both standard and vertex form, you may have noticed that the **y-intercept value is equal to the value of the c constant in the equation itself**. That is going to be true with every parabola/quadratic equation you encounter in those forms. Simply look for the c constant and that is going to be your y-intercept.

## Graph Of Displacement Vs Time

Time is usually an independent variable that other quantities, such as displacement, depend upon. A graph of displacement versus time would, thus, have *x* on the vertical axis and *t* on the horizontal axis. Figure 2 is just such a straight-line graph. It shows a graph of displacement versus time for a jet-powered car on a very flat dry lake bed in Nevada.

Figure 2. Graph of displacement versus time for a jet-powered car on the Bonneville Salt Flats.

Using the relationship between dependent and independent variables, we see that the slope in the graph above is average velocity \bar\\ and the intercept is displacement at time zerothat is, *x*0. Substituting these symbols into y=\text+b\\ gives

Thus a graph of displacement versus time gives a general relationship among displacement, velocity, and time, as well as giving detailed numerical information about a specific situation.

**Recommended Reading: What Does The Letter A Mean In Math **

## B What Is The Slope Of Your Graph And What Does The

- School
- 100%4 out of 4 people found this document helpful

* This preview shows page 2 – 4 out of 4 pages.*

##### We have textbook solutions for you!

**The document you are viewing contains questions related to this textbook.****The document you are viewing contains questions related to this textbook.**

Benjamin N Cardozo High School

PHYSICS 101

Experiment 7_ Reflection and Refraction.pdf

Lone Star College, CyFair

Benjamin N Cardozo High School PHYSICS 101

Physics Lab Report #26

Colorado State University BMS 112

Renfro_Lab9.docx

Florida Atlantic University PHY PHY2049L

Lab 8.pdf

Lone Star College, CyFair PHYSICS 2426

Experiment 7_ Reflection and Refraction.pdf

##### We have textbook solutions for you!

**The document you are viewing contains questions related to this textbook.****The document you are viewing contains questions related to this textbook.**

## What Is The Velocity On A Position Time Graph

In a position-time graph, the velocity of the moving object is represented by the slope, or steepness, of the graph line. If the graph line is horizontal, like the line after time = 5 seconds in Graph 2 in the Figure below, then the slope is zero and so is the velocity. The position of the object is not changing.

**Also Check: Geometry Dash 1 20 **

## What Does A Negative Slope Coefficient Mean

Slope is usually expressed as an absolute value. In the function y = 3x, for example, the slope is positive 3, the coefficient of x. In statistics, a graph with a negative slope represents **a negative correlation between two variables**. This means that as one variable increases, the other decreases and vice versa.

## What Does C Represent In Wave Equation

where c is **a fixed non-negative real coefficient**. A solution of this equation can be quite complicated, but it can be analyzed as a linear combination of simple solutions that are sinusoidal plane waves with various directions of propagation and wavelengths but all with the same propagation speed c.

**Read Also: Who Is Paris Jackson’s Real Father **

## What Is Slope In Physics

Slope is a mathematical term in physics that is used to describethe steepness of a line, or other physical object. Mathematically,slope is known as “m”. The basic equation is:

M = Rise/Run or M = y/x.

This is best explained by a drawing:

The run

So if you know the length of the rise, and the length of therun, you can calculate the slope by dividing the rise by therun.

Hope this helps.

## Graphing Position As A Function Of Time

A graph, like a picture, is worth a thousand words. Graphs not only contain numerical information, they also reveal relationships between physical quantities. In this section, we will investigate kinematics by analyzing graphs of position over time.

Graphs in this text have perpendicular axes, one horizontal and the other vertical. When two physical quantities are plotted against each other, the horizontal axis is usually considered the independent variable, and the vertical axis is the dependent variable. In algebra, you would have referred to the horizontal axis as the *x*-axis and the vertical axis as the *y*-axis. As in Figure 2.10, a straight-line graph has the general form y b .

Here *m* is the slope, defined as the rise divided by the run of the straight line. The letter *b* is the *y*-intercept which is the point at which the line crosses the vertical, *y*-axis. In terms of a physical situation in the real world, these quantities will take on a specific significance, as we will see below.

*y**mx**b*

In physics, time is usually the independent variable. Other quantities, such as displacement, are said to depend upon it. A graph of position versus time, therefore, would have position on the vertical axis and time on the horizontal axis . In this case, to what would the slope and *y*-intercept refer? Letâs look back at our original example when studying distance and displacement.

**You May Like: Imagine Math Parent Portal **

## What Is Delta V In Physics

What does mean in physics?, In general **physics**, delta terms change and delta-v is simply a change in velocity. The Greek uppercase letter delta is the standard mathematical symbol to **represent** change in some quantity. That is a delta and it essentially **means**, a change in. x **means** a change in x. For example say you moved 2 feet forwards.

Furthermore, What is the value of Delta V?, **Delta****v** , symbolized as **v** and pronounced **delta**-vee, as used in spacecraft flight dynamics, is a measure of the impulse per unit of spacecraft mass that is needed to perform a maneuver such as launching from or landing on a planet or moon, or an in-space orbital maneuver.

Finally, What is Delta V in electrical physics?, The change in **electric** potential as a charged object moves from point A to point B **is** defined as **delta** EPE **delta V** = charge on object. The units of **electric** potential **are** = Volts.

## How Do You Find A Slope Of An Equation

To find the slope of a line given the equation of the line, first write it in slope -intercept form. Use inverse operations to solve for y so that it is written as y=mx+b. Then you can easily see the slope since it is the coefficient of the x variable, or the number in front of x.

**Also Check: Antibonding Orbitals Khan Academy **

## The Attempt At A Solution

**A slope can not be just a random value, it must be consisted of some constants.****Thanks. **

- 74

- 4

**physical **

- 334

- 61

ddddd28 said:Actually, I have. But, I couldn’t find the relation.

ddddd28 said:The “right” answer according the teacher was that the meaning of the slope is the ratio between the difference of the tan angle and the difference of n, which is true, but in the same time, doesn’t contribute to your understanding. For example, the slope of x is the ratio between the change of distance and the time – this is mathematical meaning. The physics would say “velocity”.I am dissastified not because it might be wrong, but because the question dealt with the

physicalmeaning.

** what ****why or how**

ddddd28 said:Thanks, for all of your responses.Whether the teacher’s answer is legitimate or not, I think most of you missed the intention of the original question:” how could I find which constants the slope consists of?”

Velaargued that my intuition is right, but not knowing moments well enough, I couldn’t derive it easily. Please instruct me more specifically.

* Mg* sin= mg* r *sin sin = r* /sin by sine theorem

## What Does A Gradient Mean In Physics

I’m a physics high school student and have learned about the term ‘gradient’ regarding a few situations, such as pressure gradients and temperature gradients.

But what does this really mean? What is the physics meaning of gradient? I know that the pressure gradient is $\frac$ and the temperature gradient is $\frac$. If we take the $dx$, for instance, as an extremely small number, then the gradient approaches towards a very large value. What does this imply? Please explain in simple language!

- 2$\begingroup$Do not forget that P is a function of x, so if P is continuous, then if dx is small then dP is small too, the ratio is independent of the value of dx if dx is small enough.en.wikipedia.org/wiki/Derivative$\endgroup$ user126422Feb 24 ’17 at 3:46
- 1Feb 24 ’17 at 6:07
- 1$\begingroup$Please use mathjax to format mathematical expressions. To learn more about mathjax, please read MathJax basic tutorial and quick reference.$\endgroup$ YashasFeb 24 ’17 at 6:23
- $\begingroup$Appreciate the edits Yashas 🙂 I made a lazy choice not to, and that is on me.$\endgroup$

I struggled with the concept myself even in later calculus … which is a real problem when a meteorology major!

But one day it just dawned on me that it’s as simple as it sounds. It’s the rate of difference.

Gradient refers to how steep a line is, which is basically the slope.$\frac$ and $\frac$ are basically the derivative of a function, i.e its slope.

**Don’t Miss: Holt Geometry Chapter 7 Test Form C Answers **