Question

What is the linear function equation represented by the graph?

Answer 1

Look at the picture.

The point-slope form of a line:

$y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (0, 1) and (2, 0). Substitute:

$m=\dfrac{0-1}{2-0}=\dfrac{-1}{2}=-\dfrac{1}{2}\\\\y-1=-\dfrac{1}{2}(x-0)\\\\y-1=-\dfrac{1}{2}x\qquad|+1\\\\y=-\dfrac{1}{2}x+1$

Answer: $f(x)=-\dfrac{1}{2}x+1$