Algebra: Writing Equations of Lines
Name:_____________________________________
Write the equation of each line in slope intercept form.
To write an equation of a line in the form y = mx + b, we need two things: the slope (m) and any point on the line. There are many
methods for doing this, but I have chosen the one I believe will be easiest for you. We will be using the point – slope form of a line.
The formula is: y – y1 = m(x – x1). It is the next to last formula on your Algebra 1 formula sheet! You will use this over and over
throughout the next several years. Commit it to long-term memory now!
Example: Write the equation of the line with slope -2 that
passes through the point (5, 3).
Now you try these. For each, write the equation of the line
described:
Steps: - Find the slope and a point & plug into the formula.
- Take care of any double negatives.
- Distribute the slope.
- Move the constant (if any) that is still on the left.
- You have an equation in Slope Intercept Form!
1. Slope is
4
5
and passes through (-5, -5)
2. Slope is  72 and passes through (14, 9)
Example: Write the equation of the line with slope
2
3
that
passes through (-9, 5).
3. Passes through (0, 6) with slope -1
Example: Write the equation of the line with slope 0 that
passes through (12, -4).
4. Passes through (2, 7) with slope 0
Example: Write the equation of the line that passes through
(3, 5) with undefined slope. (This is the only tricky one for
which the formula does not work!)
5. Slope is undefined and passes through (2, -9)
What if I give you two points? How could I find the slope?
Example: Write the equation of the line that passes through
(2, -9) & (1, 5)
Example: Write the equation of the line that passes through
(9, 2) & (12, 4)
Now, you work these four. For each, find the equation of
the line through the two points:
1. (6, 15) & (1, 5)
2. (4, -11) (-3, -4)
Example: Write the equation of the line that passes through
(4, 2) & (-3, 9)
3. (9, 13) & (-3, 5)
Example: Write the equation of the line whose x-intercept is
5 and whose y-intercept is -3
4. Write an equation of the line whose x-intercept is 4 and
whose y-intercept is -5.
Algebra: Writing Equations of Lines (Parallel & Perpendicular)
Guided Practice
Write the equation of each line in slope intercept form.
Name:__________________________________
1. Parallel to y = 3x – 5 and passes through (2, -1)
4. Perpendicular to y = -2x + 5 & passes thru (8, 7)
2. Parallel to 2x – 3y = 8 & passes through (-15, 2)
5. Perpendicular to 2x – 3y = 8 & contains (-6, -3)
3. Parallel to y = -x – 7 & passes thru the x-intercept of
2x – 5y = 10.
6. Perpendicular to y = -4x + 7 thru the same y-intercept.
Algebra Homework: Writing equations of lines
Name:__________________________________
Write the equation of each line in slope-intercept form for the following line descriptions using the formula y – y1 = m(x – x1)
where applicable.
1. Slope is 3 & contains (2, -4)
8. Passes thru (3, 3) & (6, 5)
2. Passes thru (-1, -1) with slope 5
9. Passes thru (10, -7) & (5, -6)
3. Slope is
3
4
& passes thru (16, -5)
10. Passes thru (2, 1) & (5, 1)
4. Slope is 0 & passes thru (2, -3)
11. Perpendicular to y = -2x – 12 & passes thru (-6, -1)
5. Slope is undefined & passes thru (4, -2)
6. Passes thru (4, 5) & (-6, 0)
12. Perpendicular to y =
7. Passes thru (4, -1) & (9, 9)
13. Parallel to y =
2
3
2
3
x – 5 & passes thru (12, -2).
x – 5 & passes thru (12, -2)
Algebra 1 Quiz: Writing Equations of Lines
Name:________________________________
Directions: Write the equation of each line as directed. Put your final simplified answer in slope-intercept
form on the line to the LEFT of the problem. Show all work in the space provided. You may use your
formula sheet for the point-slope form of a line and the formula for the slope of a line.
__________________________1. The line with slope
2
3
that passes thru (9, -2)
__________________________2. The line with slope 0 that passes thru (3, 8)
__________________________3. The line that passes thru the points (2, 5) and (6, 13)
__________________________4. The line that passes thru (2, 0) and (0, -5)
__________________________5. The line with slope -2 that passes thru (6, -1)
__________________________6. The line that passes thru (3, 8) and (2, 9)
__________________________7. The line with slope
3
4
that passes thru (16, 5)
__________________________8. The line that passes thru (2, 1) and (5, 1)
__________________________9. The line that has undefined slope and passes thru (3, 7).
__________________________10. The line that is parallel to y = 3x + 7 and passes thru (0, 5)
__________________________Bonus (+5): The line that is perpendicular to 2x – 3y = 12 and contains the
point (-6, -1)