Question

What is an equation of the line that passes through the point (-5,7) and is parallel to the line x+5y = 10?

Answer 1

Lines are parallel if there slopes are the same or equal. Therefore the slope of the equation x + 5y = 10 can be found below

`\begin{gathered} x+5y=10 \\ 5y=-x+10 \\ y=-(1)/(5)x+2 \\ m_1=\text{slope 1=-}(1)/(5) \end{gathered}`

The equation that passes through (-5, 7) and slope of -1/5 can be found below

`\begin{gathered} m=(y-y_1)/(x-x_1) \\ m=(y-7)/(x+5) \\ -(1)/(5)(x+5)=y-7 \\ -(x)/(5)-1=y-7 \\ y=-(x)/(5)-1+7 \\ y=-(x)/(5)+6 \end{gathered}`