Finding linear function

Question

Find the linear function h, given h(1)= -1 and h(-2) = 14. Then find h(3)

Answer 1

Use slope-intercept form h(x) = mx+b, where m represents the slope and b the y-intercept. They gave us two points (1,-1) and (2,14).

 

First find the slope using the two points.

 

m = rise/run

= h(x2) - h(x1) / x2 - x1 

= (14 - (-1))/(-2 -1)= 15/-3 = -5

 

 

Now find the intercept using the slope and either point.

 

h(x) = -5x + b and (1, -1)

-1 = -5(1) + b

4 = b

 

So the function is h(x) = -5x +4 and you can use this to find h(3).

h(3) = -5(3) +4 = -15 +4 = -11