1. Day 7 – Parallel and Perpendicular lines

2. Parallel Lines
If two different lines have the same slope, the lines are parallel. If two non-vertical lines are parallel, they have the same slope. Two parallel, vertical lines have undefined slopes.

3. Perpendicular Lines
If the slope of two lines are m and − 1 𝑚 , lines are perpendicular. If the slope of a line is m, then the slope of a line perpendicular to it is − 1 𝑚 .

4. Example 1
Find the equation for the line that contains point (4, 5) and is a) Parallel to the line 2𝑥+3𝑦=7. b) Perpendicular to the line 2𝑥+3𝑦=7.

5. Answer
a) First, write the equation of the given line in slope-intercept form.

6. Answer
The slope of the line is − Any line parallel to this line must also have a slope of − The coordinates of the given point are (4, 5), and the slope is − Now use the point-slope form to write an equation for the parallel line through the given point. Substitute − for m and (4, 5) for (𝑥 1 , 𝑦 1 )into the point- slope form of the equation.

7. Answer
b) When a line has slope − 2 3 , any line perpendicular to that line has slope Since the line also contains the point (4, 5), you can substitute for m and (4, 5) for ( 𝑥 1 , 𝑦 1 ) in 𝑦− 𝑦 1 =𝑚(𝑥− 𝑥 1 ).

8. Answer
As a check, check the equations 𝑦−5=− 2 3 (𝑥−4)and 𝑦−5= 3 2 (𝑥−4) to slope-intercept form. Graph the lines using a square window. The lines will appear perpendicular. Both lines will also contain the point (4, 5) where they intersect.