If f(x) is a linear function, f(-1) = -3, and f(3) =3, find and equation for f(x)

Answer 1

Based on the given values the points oft this line are: (-1,-3) and (3,3)

First find the slope:

m = (y₂ - y₁)/(x₂ - x₁) = (3 - (-3))/(3 - (-1)) = 6/4 = 3/2

Substitute into slope intercept form of a linear equation - use point 2:

y = mx + b

3 = 3(3/2) + b

b = 3 - 9/2 = -3/2

Equation is:

y = (3/2)x - 3/2

Answer 2

f(-1) = -3

the point (-1,-3)

f(3) = 3

the point (3,3)

a line through them has slope = (3+3)/(3+1) = 6/4=3/2

y-3 = (3/2)(x-3) in point slope form

y = (3/2)x -9/2+3

y = (3/2)x - 3/2 in slope intercept form

Answer 3

Need f(x) = mx+b to be a linear equation.

Points (-1,-3) and (3,3)

m = (y₂-y₁)/(x₂-x₁) = (3 - -3)/(3 - -1) = 6/4 = 3/2

y-3 = (3/2)(x-3) = 3x/2-9/2

f(x) = y = 3x/2-3/2

Answer 4

Since f(-1) = -3 and f(3) = 3, the points (-1, -3) and (3,3) are on the line.

Slope = [3 - (-3)] / [3 - (-1)] = 6/4 = 3/2

Equation of line: y - 3 = (3/2)(x - 3)

y = f(x) = (3/2)x - 3/2