The equation of a line in slope-intercept form is given by
[tex]y=mx+b[/tex]
so
step 1
Find out the slope m
we take two points from the table
(2,3) and (5,9)
[tex]\begin{gathered} m=\frac{9-3}{5-2} \\ \\ m=\frac{6}{3} \\ \\ m=2 \end{gathered}[/tex]
step 2
Find out the value of b
we have
m=2
point (2,3)
substitute and solve for b
[tex]\begin{gathered} 3=2(2)+b \\ 3=4+b \\ b=-1 \end{gathered}[/tex]
The linear equation is
[tex]f(x)=2x-1[/tex]
step 3
Find out the value of k
For x=-2
[tex]\begin{gathered} f(x)=2(-2)-1 \\ f(x)=-4-1 \\ f(x)=-5 \end{gathered}[/tex]
therefore
The value of k=-5
