Question

Find a linear function h, given h(5) = - 7 and h( - 1) = 11. Then find h(1).

Answer 1

`h(1) =(29)/(3)` or
`h(1) =9.67`

Explanation:

h(5) = - 7 --> (5, 7)

h( - 1) = 11 --> (-1, 11)

Using those two points to find the slope:

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

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

`m =(11-7)/((-1)-5)`

`m =(4)/(-6)`

`m =-(2)/(3)`

`(5, 7)`

`y = mx + b`

`y=-(2)/(3)x+b`

`7=-(2)/(3)(5)+b`

`7=-(10)/(3)+b`

`3(7=-(10)/(3)+b)`

`21=-10+3b`

`+10`
`+10`

`31=3b`

`/3`
`/3`

`(31)/(3) =b`

`y=-(2)/(3)x+(31)/(3)`

`h(1) =-(2)/(3)(1)+(31)/(3)`

`h(1) =-(2)/(3)+(31)/(3)`

`h(1) =(29)/(3)`

`h(1) =9.67`

Hope this helps!