1. Parallel Lines

2. Parallel Lines never intersect have no points in common
have the same slope
have different y-intercepts

3. Common Questions
Q: What is the slope of a line parallel to a line with a slope of 5?
A: Since parallel lines have equal slopes, the answer would be 5.
Q: What’s the slope of a line parallel to a line with a slope of – 3?
A: Slope = – 3

4. Common Questions
Q: What is the slope of a line parallel to the line y = 2x + 5?
Remember the slope-intercept equation of a line
y = mx + b
where m is slope and b is the y-intercept.
A: In this equation, the slope is 2 since y = 2x + 5.
Since parallel lines have equal slopes, the answer would be 2.

5. Common Questions Q: What is the slope of a line parallel to the line
12x + 2y=17?
Since parallel lines have equal slopes, we first have to
put this equation in slope-intercept form.
A: Move the x-term 2y = – 12x + 17
Divide by y = – 6x + we don’t care
The slope of both this line and it’s parallel is – 6.

6. y – 4 = 2( x – 3) distribute the 2
Common Questions
Q: What is the equation of a line parallel to the line y = 2x + 5
and passing through the point (3, 4)?
It’s the same as asking “What is the equation of a line
with a slope of 2 and passing through the point (3, 4)?”
A: We have a point and a slope, we’ll use the point-slope equation of a line. y – y1 = m( x – x1 )
y – 4 = 2( x – 3) distribute the 2
y – 4 = 2x – add 4 to each side
y = 2x – 2
Read carefully! Sometimes they ask for slope, and sometimes they ask for the equation of the line.

7. Common Questions
Q: What is the equation of a line parallel to the line y = 5
and passing through the point (3, 4)?
y = 5 is the same as y = 0x + 5 because we have no x.
A: We have a point and a slope, we’ll use the point-slope
equation of a line. y – y1 = m( x – x1 ) m = 0, x = 3, y = 4
y – 4 = 0( x – 3) zero times anything is zero
y – 4 = add 4 to each side
y = 4
NOTICE: both lines are in the form y = a number.
There’s also another way to think of this problem …

8. Common Questions Q: A different approach to the question:
“What is the equation of a line parallel to the line y = 5
and passing through the point (3, 4)?
y = 5 is a horizontal line so a parallel line will also be horizontal.
A: We need a line in the format y = a number
that passes through (3, 4).
There’s only one y in town! (3, 4)
Answer: y = 4
NOTICE: The slope is 0 but the equation is y = 4.

9. Common Questions Q: What is the equation of a line parallel to the
line x = 5 and passing through the point (3, 4)?
x = 5 is a vertical line with an undefined slope.
A parallel line will also be vertical.
A: We need a line in the format x = a number
that passes through (3, 4).
There’s only one x in town! (3, 4)
Answer: x = 3
NOTICE: The slope is undefined but the equation is x = 3.

10. That’s all there is to parallel line problems!