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### Course: 8th grade (Illustrative Mathematics) > Unit 3

Lesson 1: Lesson 3: Representing proportional relationships# Graphing proportional relationships from a table

Let's graph a proportional relationship from a table of values. The graph of a proportional relationship is a line, so we can graph from any 2 points in the table. The slope of the line represents the unit rate, so changes in x and y values determine the slope. Created by Sal Khan.

## Want to join the conversation?

- guys i don't know how to graph still is that imbaressing?(13 votes)
- NO. It is not embarrassing. Graphing points is a simple thing to do. When you have a pair of coordinates, the first number is the X axis and the second number is the Y axis. To remember which number goes with what axes, just remember that X comes before Y in the alphabet. On the graph, each axes will have numbers on it. The number on the pair of coordinates, corresponds to the number on the graph. For example: A random pair coordinates that was given was (9,2). The fist number is the X axis and the value is nine. I find number 9 on the X axis and wait there. The second number is 2, so from the 9 go up to the 2 on the Y axis. One you place to dot, you are done.(22 votes)

- Am I the only one who watched the video like ten

times.(17 votes)- Now that you say it, maybe I should too...(5 votes)

- Wouldn't you have to divide 1/6 to get the slope ? For example, 1 divided by 6 which would be .166 or is that what I would do to figure out the average rate of change?(0 votes)
- No, no, you do not have to! Let me show you and easy way that my teacher always taught me:

The slope is Rise/Run (Rise over Run). This means that if you have a point on your linear graph, if you go up Rise, then over Run, you get another point on the line! Lets do it with 1/6...

Say you have a point of a line on a graph, (1,2) and you know that the slope is 1/6. Simply go up 1 from that point and right 6. This would end us up at (7,3). Now you have to points to graph your equation. You can also go down 1 then left 6 and get the same answer. Every time you go down though, it is adding negative (-) and every time you go left it is adding (-), and negative/negative is positive, that is why down, then left works.

To further answer your question, 1/6 is exactly the same as .16666... but is simpler to look at that .16666... 1/6 is a fraction and doesn't need to be a decimal! It takes some getting used to. And, .16666... is for every 1 unit on the x axis, go .16666. It is the same graph if you did it this way, but it would take a lot more work plotting that .166666 then .33333. It is easier just to use rise over run. Try it out on a few problems, it may help you out!(30 votes)

- I thank I don't like math(8 votes)
- I'm so sorry, could you please tell the formula for finding slope again? I am sorry I am asking this question :((6 votes)
- rise over run,

(**Y final**minus**Y initial**) over (**X final**minus**X initial**),

or ΔY/ΔX.(3 votes)

- whats the formula for slope?(3 votes)
- The slope is the change in y-value (or rise) divided by the change in x-value (or run).

For two points (x_1, y_1) and (x_2, y_2), the rise is y_2 - y_1, and the run is x_2 - x_1.

So the slope m of the line through these points is given by the formula

m = (y_2 - y_1) / (x_2 - x_1).

Note that the subscripts “1” and “2” can appear in either order, as long as the**same**order is used for the numerator and the denominator.

Have a blessed, wonderful day!(5 votes)

- Could you keep showing examples like these but also harder examples because when I go to do the actual work there are complicated decimals and fractions, not just whole numbers.(4 votes)
- Ca someone pls explain this to me in actual english(4 votes)
- At no point in any of the videos of the lesson is slope taught...(4 votes)
- what is slope?

(I think he explained it in the video, but he was talking kinda fast.)(3 votes)- The slope of a line is a measure of its steepness or its Gradient.(2 votes)

## Video transcript

We're asked to graph the
proportional relationship shown in the table below. And they give us a
table of x values, and the corresponding y values. So we see when x is equal
to 0, y is equal to 0. Then they give us a
bunch of other points. When x is 3, y is 0.5. When x is 6, y is 1,
so on and so forth. So let's graph one of
these that actually have integer values
for both coordinates. So when x is 6, y is 1. So we only need two points
to specify the line. So we've actually graphed it. But then they also ask us,
what is the slope of this line? And we just have to
remind ourselves. Our slope is what is our change
in y for a given change in x. So, for example, or another
way to think about it, what is your change in
y over your change in x? So here, our x changed by 6. It went from 0 to 6. And our y changed by 1. So our change in
y over our change in x, which is the definition
of slope, our change in y is 1, when our change in x is 6. See that right over here. Change in y, 1 when
our change in x is 6. Let's check our answer. We got it right.