Answer:
D
[tex]y=-\frac{1}{4}x[/tex]
Step-by-step 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:
[tex]m=slope=\frac{rise}{run}=\frac{change-in-y}{change-in-x}[/tex]
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:
[tex]m=slope=\frac{rise}{run}=\frac{-1}{4}=-\frac{1}{4}[/tex]
Thus, our slope would be -1/4. Plugging into our equation for the line we get:
[tex]y=-\frac{1}{4}x[/tex]
Thus, our equation would be [tex]y=-\frac{1}{4}x[/tex].
Our answer would be D [tex]y=-\frac{1}{4}x[/tex].
I hope you find my answer to be helpful. Happy studying.
