Write Equations of Parallel and Perpendicular Lines Goals: Writing Equations of Parallel Lines Writing Equations of Perpendicular Lines

What Do Parallel Lines Have in Common? Lets Look at two parallel lines… Notice anything? Both Lines have different y-intercepts, but they have the SAME SLOPE… 𝒚= 𝟏 𝟑 𝒙+𝟔 𝒚= 𝟏 𝟑 𝒙−𝟏

So for Parallel Lines… Two Lines are Parallel if they have the exact same slope. Slopes of Horizontal lines would both be Zero. Slopes of Vertical Lines would both be undefined.

Perpendicular Lines Remember: Perpendicular lines are two lines that intersect at Right Angles. Lets Look at a pair of Perpendicular Lines. Do they have anything in common? Slopes are different and y-intercepts can be also…

Compare: 𝑦= 1 2 𝑥 𝑚= 1 2 Notice the Slopes are negative Reciprocals of each other. 𝑦=− 2 1 𝑥+3 𝑚=− 2 1 Flip Fraction and change the signs for Perpendicular Slopes!

Write the Equation of a perpendicular line passing through a point Write the equation of the line with the Perpendicular Slope and y-intercept. Find the Slope of the Original Line Find the Perpendicular Slope. Use the Perpendicular Slope and the Coordinate to find the y-intercept.