Please help!! No links

Explanation:

All of the answer choices are in the form y = mx+b, which is slope intercept form.

The given items that

means that we have these two points

Let's apply the slope formula to find m

m = (y2-y1)/(x2-x1)

m = (57-(-15))/(7-4)

m = (57+15)/(7-4)

m = 72/3

m = 24 is the slope

Then apply point-slope form and solve for y

y - y1 = m(x - x1)

y - (-15) = 24(x - 4)

y + 15 = 24(x - 4)

y + 15 = 24x - 96

y = 24x - 96 - 15

y = 24x - 111

f(x) = 24x - 111 , which is choice D

We can verify this by plugging x = 4 into choice D

f(x) = 24x - 111

f(4) = 24*4 - 111

f(4) = 96 - 111

f(4) = -15, which works out

Repeat for x = 7. We should get an output of 57

f(x) = 24x - 111

f(7) = 24*7 - 111

f(7) = 168 - 111

f(7) = 57, so that works out as well

Both of the original equations your teacher gave are proven to be true when f(x) = 24x-111 which confirms we have the correct linear function.

If you're in a hurry, you can skip the previous section and simply plug x = 4 into each answer choice. Then eliminate any answer choices that don't have an output of y = -15. The same would apply for x = 4 leading to y = 57. Only choice D will be left standing after everything else is eliminated.

b, i believe, but not sure.