Answer: f(x) = 24x - 111, choice D
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Step-by-step 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
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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.