Question

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Which graph shows a proportional relationship between x and y?

Answer 1

Answer:

C

Step-by-step explanation:

The y-axis is the vertical axis, which is represented by y, and the x-axis the horizontal axis, represented by x. You can see in the graph that (3, 12) is one point. 3 x 4 = 12, where x is 3 and y is 12. This proves the proportional relationship with x and y is y = 4x. To double check, you can plug in (3, 12) to get 12 = 4(3). 4 x 3 = 12, so Option C shows the proportional relationship.

Answer 2

Linear Equations

We typically write linear equations in slope-intercept form:

$y=mx+b$

• m = slope
• b = y-intercept (the value of y when x=0)

Because this graph has a proportional relationship, it means that they pass through the point (0,0), and that our y-intercept is 0. Our equation looks like this:

$y=mx$

Solving the Question

First, we typically find the slope of the equation using the slope formula:

$m=\dfrac{y_2-y_1}{x_2-x_1}$ where $(x_1,y_1)$ and $(x_2,y_2)$ are two points that fall on the line

⇒ Plug in any two points that the line passes through, such as (0,0) and (3,12):

$m=\dfrac{12-0}{3-0}\\\\m=\dfrac{12}{3}\\\\m=4$

Therefore, the slope of the line is 4. Plug this into $y=mx$:

$y=4x$

Answer

$y=4x$