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=(y_2-y_1)/(x_2-x_1)`

Substitute:

`m=(4-8)/(-1-(-4))=(-4)/(3)=-(4)/(3)\\\\y-8=-(4)/(3)(x-(-4))\\\\y-8=-(4)/(3)x-(16)/(3)\ \ \ \ |+8\\\\y=-(4)/(3)x-(16)/(3)+(24)/(3)\\\\y=-(4)/(3)x+(8)/(3)\ \ \ |\cdot3\\\\3y=-4x+8\ \ \ |+4x\\\\4x+3y=8`

The slope-intercept form:
`y=-(4)/(3)x+(8)/(3)`

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