Question

Write a linear function F with f(-9)=10 and f(-1)=-2

Answer 1

Answer:

$f(x)=-1.5x-3.5$

Step-by-step explanation:

Let

x ----> the input value (independent variable)

y ----> the output variable (the dependent variable)

we have

f(-9)=10 and f(-1)=-2

so

we have the points

(-9,10) and (-1,-2)

step 1

Find the slope m

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{-2-10}{-1+9}$

$m=\frac{-12}{8}$

$m=-1.5$

step 2

Find the equation of the line in slope point form

$y-y1=m(x-x1)$

we have

$m=-1.5$

$(x1,y1)=(-1,-2)$

substitute the values

$y+2=-1.5(x+1)$

$y+2=-1.5x-1.5$

$y=-1.5x-1.5-2$

$y=-1.5x-3.5$

Write in function notation

$f(x)=-1.5x-3.5$