Question

F(-4)=8 and f(-1)=4 write the linear equation

Answer 1

$f(-4)=8\to(-4,\ 8)\\\\f(-1)=4\to(-1,\ 4)$

The point-slope formula of a line:

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

Substitute:

$m=\dfrac{4-8}{-1-(-4)}=\dfrac{-4}{3}=-\dfrac{4}{3}\\\\y-8=-\dfrac{4}{3}(x-(-4))\\\\y-8=-\dfrac{4}{3}x-\dfrac{16}{3}\ \ \ \ |+8\\\\y=-\dfrac{4}{3}x-\dfrac{16}{3}+\dfrac{24}{3}\\\\y=-\dfrac{4}{3}x+\dfrac{8}{3}\ \ \ |\cdot3\\\\3y=-4x+8\ \ \ |+4x\\\\4x+3y=8$

The slope-intercept form: $y=-\dfrac{4}{3}x+\dfrac{8}{3}$

The standard form: $4x+3y=8$