5.5 Parallel & Perpendicular lines

If 2 non-vertical lines in the same plane have ___________________, then
they are _____________

If 2 non-vertical lines in the same plane are ________________, then they
have the _______________
Ex 1:
Write an equation of the line that passes through (-3,-5) and is parallel to the line
𝑦 = 3𝑥 − 1.
Step 1: ____________________
The parallel line through (-3,-5) has a slope of _____
Step 2: Find the y-intercept using the ______________ and _______________.
Step 3: Write an equation of the parallel line to 𝑦 = 3𝑥 − 1. _________________.
Practice:
1. Write an equation of the line that passes through (-2,11) and is parallel to
the line 𝑦 = −𝑥 + 5
2. Write an equation of the line that passes through (5,-1) and is parallel to the
3
line 𝑦 = − 5 𝑥 − 3

If 2 non-vertical lines in the same plane have slopes that are
____________ ______________, then the lines are _______________.

If 2 non-vertical lines in the same plane are ____________________, then
their slopes are _____________ ______________.
Ex 2:
Determine which lines, if any, are parallel or perpendicular
line a: 𝑦 = 5𝑥 − 3
line b: 𝑥 + 5𝑦 = 2
line c: −10𝑦 − 2𝑥 = 0
Find the slopes of each line (put in slope intercept form).
Practice:
3. Determine which lines, if any, are parallel or perpendicular
line a: 2𝑥 + 6𝑦 = −3
line b: 𝑦 = 3𝑥 − 8
line c: −1.5𝑦 + 4.5𝑥 = 6
4. Determine which lines, if any, are parallel or perpendicular
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line a 𝑦 = 5 𝑥 + 1
line b: 5𝑦 = 3𝑥 − 2
line c: 10𝑥 − 6𝑦 = −4
Ex. 4:
Write an equation of the line that passes through (4,-5) and is perpendicular to the
line 𝑦 = 2𝑥 + 3
Step 1: Identify the slope
So, the slope of a line perpendicular should be ___________
Step 2: Find the y-intercept using _________ and ________________
Step 3: Write an equation (slope-intercept form) __________________
Practice:
5. Is line a perpendicular to line b. justify your answer with work
Line a: 2𝑦 + 𝑥 = −12
line b: 2𝑦 = 3𝑥 − 8
6. Write an equation of the line that passes through (4,3) and is perpendicular
to the line 𝑦 = 4𝑥 − 7
7. Write an equation of the line that passes through (-5,2) and is perpendicular
to the line 𝑦 + 3 = 2𝑥