Question

Write an equation for the linear function f(x) using the given information. ———————————————Using the points 2,0 & 4,3

Answer 1

To find the equation in the form

`y=mx+b`

the slope is defined by:

`\begin{gathered} m=(y2-y1)/(x2-x1) \\ m=(3-0)/(4-2) \\ m=(3)/(2) \end{gathered}`

To find b you can replace any of the points on the equation an clear for b

(x,y)=(4,3)

`\begin{gathered} y=(3)/(2)x+b \\ 3=(3)/(2)\cdot4+b \\ 3=6+b \\ 3-6=b \\ b=-3 \end{gathered}`

to check if the answer is correct replace 2 as x in the equation.

`\begin{gathered} y=(3)/(2)\cdot2-3 \\ y=3-3 \\ y=0 \end{gathered}`

since the answer was 0 and point was 2,0 the equation is correct.