Write a linear function f with the values f(−2)=3 and f(5)=7.

Answer 1

A linear equation is written in the form y = mx + b, where "m" is the slope of the line and "b" is the y-intercept. The function, f(x), is also known as "y". We have 2 equations with 2 unknowns, so this can be solved.

Eq. 1: f(x) = mx + b

f( -2) = -2m + b = 3

3 = -2m + b

Eq. 2: f(x) = mx + b

f(5) = 5x + b =7

7 = 5x + b

Using the elimination method we can solve for "m":

3 = -2m + b

-(7 = 5m + b)

-4 = -7m + 0

-4/-7 = m

m = 4/7

Using this value of "m" in either equation we can solve fo "b":

3 = -2(4/7) + b

3 + 8/7 = b

21/7 + 8/7 = b

b = 29/7

Therefore, your equation is: y = (4/7)x + 29/7. Usually we don't leave an equation with fractions, so if we multiply everything by 7 we get: 7y = 4x + 29--->4x - 7y + 29 = 0.

Hope this helps!

Answer 2

Use two-point form

(y - 3) / (x + 2) = (7 - 3) / (5 + 2)