Question

Can someone please explain?

Answer 1

Hello!

The answer is:

The correct option is the first option:  

$y=-4x+64$

Why?

To write the equation of the line in slope-interception  form we need to extract all the information that we need from the graphic.

We must remember that the slope-interception form of the lines is:

$y=mx+b$

Where,

y, is the function

m, is the slope of the line

x, is the variable

b, is the y-axis intercept

We can find the slope using the following formula:

$m=\frac{ChangeInY}{ChangeInX}$

Which is for this case:

$m=\frac{64}{16}=4$

As we can see from the graphic, the line is decresing, so the sign of the slope "m" will be negative, so:

$m=-4$

We can find the value of "b" seeing where the line intercepts the y-axis.

As we can see it intercept the y-axis at:  $y=64$

Then, now that we already know the value of "m" and "b", we can write the equation of the line:

$y=mx+b=-4x+64\\y=-4x+64$

So, the correct option is the first option:

$y=-4x+64$

Have a nice day!