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

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

User Martina
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