Question

Find a linear function h, given h(3) = - 4 and h( - 2) = 16. Then find h(2).

Answer 1

express in coordinate pairs: (x,y)

h(3) = - 4 ⇒ 3,-4

h( - 2) = 16 ⇒ -2, 16

`\tt slope=(y_2-y_1)/(x_2-x_1)=(16-(-4))/(-2-3)=(20)/(-5)=-4`

equation:

`\tt y-y_1=m(x-x_1)\rightarrow m=slope\\\\y+4=-4(x-3)\\\\y=-4x+8`

for h(2):

`\tt y=-4(2)+8=0`

h(2) = 0