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=(y2-y1)/(x2-x1) \\ m=(9-6)/(4-(-2)) \\ m=(3)/(6)=(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=(1)/(2)\cdot(-2)+b \\ 6=-1+b \\ 6+1=b \\ b=7 \end{gathered}`

the equation should be

`y=(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=(1)/(2)(-4)+7 \\ y=-2+7 \\ y=5 \end{gathered}`

with this we can conclude the equation is correct.