Question

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

H(x)=?

Answer 1

Answer:

h(x) = -5x + 6

h(6) = -24

Step-by-step explanation:

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

$y=mx+b$

m - slope

b - y-intercept

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

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:

$m=\dfrac{26-(-29)}{-4-7}=\dfrac{55}{-11}=-5$

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:

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