Question

Write an equation for the linear function f(x) using the given information.

Answer 1

To fins the linear equation you shoul use two of the points to find the slope

a=(-2,6) b=(4,9)

and use the formula for the slope in this way

$\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ m=\frac{9-6}{4-(-2)} \\ m=\frac{3}{6}=\frac{1}{2} \end{gathered}$

after you have the slope you can use whichever point you want to find b

y=mx+b

lets use point (-2,6)

$\begin{gathered} 6=\frac{1}{2}\cdot(-2)+b \\ 6=-1+b \\ 6+1=b \\ b=7 \end{gathered}$

the equation should be

$y=\frac{1}{2}x+7$

to check if the answer is correct we can replace in the equation with one of the point; lets use (-4,5)

$\begin{gathered} y=\frac{1}{2}(-4)+7 \\ y=-2+7 \\ y=5 \end{gathered}$

with this we can conclude the equation is correct.