Question

Write a linear function f with f(−9)=10 and f(−1)=−2

Answer 1

First we need to find the slope of the function

The slope of a function is equal to

$\frac{f(x_2)-f(x_1)}{x_2-x_1}$

So now we plug this into the equation and find the slope (M will represent the slope)

$m=\frac{10--2}{-9--1}\\m=\frac{12}{-8}\\m=-\frac{3}{2}$

So the slope is -3/2

Now we can use point-slope form.

Point slope form is represented by

$Y-Y_1=m(X-X_1)$

So when we plug in our values we get

$Y--2=-3/2(X--1)\\Y+2 = -3/2(X+1)\\Y+2 = -3/2X-3/2\\Y=-3/2X-7/2$

So the equation is

Y = -3/2X-7/2