Question

Write a linear equation that passes through the points (3,1) and (-2,6)

Answer 1

The general equation of a line is

`y=mx+b`

where m is the slope and b the y-intercept

we can find m by the formula

`m=(y2-y1)/(x2-1)`

where (x2,y2) is a right point of (x1,y1) then if we replace the point of the exercise we can find the slope of the line

`\begin{gathered} m=(1-6)/(3-(-2)) \\ \\ m=(-5)/(5)=-1 \end{gathered}`

value of the slope is -1

now to find y-intercept or b we replace the slope and a point of the line on the general equation

for example i will use (3,1)

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

no we can replace the slope -1 and b 4 on the general equation to have the equation of the line to the exercise

`\begin{gathered} y=-x+4 \\ \end{gathered}`