Question

Which equation represented the line shown on the coordinate plane below?

Answer 1

D

`y=-(1)/(4)x`

Explanation:

So we are given a line and are asked to find the equation for the line. To do this we need 2 things: the slope and a point on the line (preferable the y-intercept). Remember, the equation for a line in y-intercept form is:

y = mx + b

Where m is the slope and b is the y-intercept.

From looking at the image, we can see that the line intercepts the y-axis at y = 0. Thus, the y-intercept is 0. So our equation for the line becomes:

y = mx

Where m is the slope. Now we must find the slope in order to find the equation for the line. Remember:

`m=slope=(rise)/(run)=(change-in-y)/(change-in-x)`

Notice how the y-value of the line decreases by 1 when the x-value increases by 4. This means that we can use the -1 for the rise (or the change in y) and 4 for the run (or the change in x). Plugging in we get:

`m=slope=(rise)/(run)=(-1)/(4)=-(1)/(4)`

Thus, our slope would be -1/4. Plugging into our equation for the line we get:

`y=-(1)/(4)x`

Thus, our equation would be
`y=-(1)/(4)x`.

Our answer would be D
`y=-(1)/(4)x`.

I hope you find my answer to be helpful. Happy studying.