If f(x) is a linear function, f(-4)=0. and f(3) = -2, find an equation for f(x).

Answer 1

Linear function means the function has this shape: f(x)=Ax+B. Then, when

x=-4, f(-4)=0=A(-4)+B=-4A+B

x=3, f(3)=-2=A(3)+B=3A+B

We have a system of equations

A=-2/7

B=-8/7

Answer 2

(-4,0) (3,-2) have line through them with slope = y change over x change = m = 2/-7 = -2/7

y = (-2/7)(x+4)

y = -2x/7 -8/7

or

7y = -2x -8

or

2x +7y = -8 in standard form

or

2x +7y +8= 0 in general form