Please help me! Given two points on the line, input the equation of the line in standard form Ax + By = C. Reduce all fractional answers to lowest terms.

(-8, 0), (1, 5)

Question

Please help me! Given two points on the line, input the equation of the line in standard form Ax + By = C. Reduce all fractional answers to lowest terms.

(-8, 0), (1, 5)

anonymous · Answer

Please help!

anonymous · Answer

Slope of line through the two points is:
$$m=\frac{ y _{2} -y _{1} }{  x _{2} -x _{1} }=\frac{ 5-0 }{ 1-(-8) }=\frac{ 5 }{ 9 }$$
Using the point slope form of the equation of a line:
$$y-y_{1}=m(x-x_{1}) \rightarrow y-0=\frac{ 5 }{ 9 }(x+8 )$$
Multiply both sides of the equation by 9 and rearranging:
$$9y=5x+40 \rightarrow -5x+9y=40$$