Question

Find a linear function h,given h(7)=-29 and h(-4)=26 then find h(6)

H(x)=?

Answer 1

h(x) = -5x + 6

h(6) = -24

Explanation:

The slope-intercept form of an equation of a line:

`y=mx+b`

m - slope

b - y-intercept

The formula of a slope:

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

We have

`h(7)=-29\to x=7,\ y=-29\\\\h(-4)=26\to x=-4,\ y=26`

Substitute to the formula of a slope:

`m=(26-(-29))/(-4-7)=(55)/(-11)=-5`

Put m = -5, x = 7 and y = -29 ot the equation of a line:

`-29=(-5)(7)+b`

`-29=-35+b` add 35 to both sides

`6=b\to b=6`

Finally

`y=-5x+6`

h(6) → put x = 6 to the equation of a line:

`h(6)=-5(6)+6=-30+6=-24`