Question

Find the value of k in the data set so that f (x) is a linear function.

Answer 1

The equation of a line in slope-intercept form is given by

`y=mx+b`

so

step 1

Find out the slope m

we take two points from the table

(2,3) and (5,9)

`\begin{gathered} m=(9-3)/(5-2) \\ \\ m=(6)/(3) \\ \\ m=2 \end{gathered}`

step 2

Find out the value of b

we have

m=2

point (2,3)

substitute and solve for b

`\begin{gathered} 3=2(2)+b \\ 3=4+b \\ b=-1 \end{gathered}`

The linear equation is

`f(x)=2x-1`

step 3

Find out the value of k

For x=-2

`\begin{gathered} f(x)=2(-2)-1 \\ f(x)=-4-1 \\ f(x)=-5 \end{gathered}`

therefore

The value of k=-5