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### Course: Equations & Inequalities 229-236>Unit 2

Lesson 1: Graphing 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?
• 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.
• Am I the only one who watched the video like ten
times.
• Now that you say it, maybe I should too...
• 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?
• 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!
• I'm so sorry, could you please tell the formula for finding slope again? I am sorry I am asking this question :(
• rise over run,
(Y final minus Y initial) over (X final minus X initial),
or ΔY/ΔX.
• whats the formula for slope?
• 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!
• 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.
• Ca someone pls explain this to me in actual english