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Please help me find the equations for the parallel line and the perpendicular line. :(

Please help me find the equations for the parallel line and the perpendicular line-example-1
User Buena
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Given the equation of a line, you can find the equation of a line perpendicular to it, knowing the following: The product of the slopes of the lines is -1, it means that:


m1\cdot m2=-1

We already know the value of the first slope (which is the slope of the given line). Use this value to find the slope of the perpendicular line:


\begin{gathered} -(5)/(3)\cdot m2=-1 \\ m2=-1\cdot-(3)/(5) \\ m2=(3)/(5) \end{gathered}

The slope of the perpendicular line is 3/5. Use this slope and the given point, to find the equation of the perpendicular line using the point slope formula, this way:


\begin{gathered} y-y1=m(x-x1) \\ y-4=(3)/(5)(x-(-5)) \\ y-4=(3)/(5)x+3 \\ y=(3)/(5)x+7 \end{gathered}

The equation of the perpendicular line is:


y=(3)/(5)x+7

To find the equation of the line that is parallel to the given line, use the following information: parallel lines have the same slope, it means:


m1=m2

m1 has a value of -5/3, it means the parallel line also has a slope of -5/3.

Use this slope and the given point in the point slope formula, this way:


\begin{gathered} y-4=-(5)/(3)(x-(-5)) \\ y-4=-(5)/(3)x-(25)/(3) \\ y=-(5)/(3)x-(25)/(3)+4 \\ y=-(5)/(3)x-(13)/(3) \end{gathered}

The equation of the parallel line is:


y=-(5)/(3)x-(13)/(3)

User Kemen Paulos Plaza
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