This document provides instruction on writing equations of lines using different forms: slope-intercept, point-slope, two-point, and intercept forms. Examples are given for writing equations of lines when given characteristics like slope, points, or intercepts. The last section presents an application example of using line equations to determine if two sets of bones found in an excavation site are parallel.

1. Writing Equations of Lines
Prepared by: Ms. Ma. Irene g. gonzales
1. Standard Form
2. Slope-intercept Form
3. Point-slope Form
4. Two-point Form
5. Intercepts Form

2. Slope – intercept Form
Let’s Practice!
Write an equation of the line given the slope
and containing the given y-intercept. Express the
equation in the form y = mx + b and in standard
form.
a. m = -4, b = 7
b. m = 2/5, b = -8
c. m = -6, b = 4
Learning Objective: Students should be able to write the equation of a line in slope-intercept form.

3. Slope – intercept Form
Let’s Practice!
Find the equation in standard form of the line
passing through (0, -5) and whose slope is 4/5.
Find the equation in standard form of the line
passing through (0, 8) and whose slope is 3/4.
Learning Objective: Students should be able to write the equation of a line in slope-intercept form.

4. Slope – intercept Form
Let’s Practice!
Write an equation of a line whose y-intercept is
3/5 and slope is -9/2. Express your answer in
standard form.
Write an equation of a line whose y-intercept is -3
and slope is 5/9. Express your answer in standard
form.
Learning Objective: Students should be able to write the equation of a line in slope-intercept form.

5. Point-slope Form
The equation of the line passing through (x1, y1)
with slope m is given by
y – y1 = m(x – x1)
Let’s Practice!
1. Find the equation of the line that passes
through (5, 8) and with slope 4. Write the
equation in standard form.
Learning Objective: Students should be able to write the equation of a line in point-slope form.

6. Point-slope Form
The equation of the line passing through (x1, y1)
with slope m is given by
y – y1 = m(x – x1)
Let’s Practice!
2. Find the equation of the line that passes
through (4,7) and with slope 5/2. Write the
equation in standard form.
Learning Objective: Students should be able to write the equation of a line in point-slope form.

7. Take the challenge!
Find the equation of the line that contains the
point (3, 4) and:
a. Parallel to y – 3x = 6
b. Perpendicular to 5x – 2y = 8
c. Parallel to y – 4x = 8
d. Perpendicular to 3x – 4y = 12
Learning Objective: Students should be able to write the equation of a line in point-slope form.

8. Two – Point Form
)(
)(
)(
1
12
12
1 xx
xx
yy
yy 



Where (x1, y1) and
(x2, y2) are two points
on the line such that
21 xx 
1. Write an equation of the line passing through
the points (1, -6) and (9, -2). Express your
answer in standard form.

9. Two – Point Form
)(
)(
)(
1
12
12
1 xx
xx
yy
yy 



21 xx 
2. Write an equation of the line passing through
the points (3, 2) and (5, -4). Express your answer
in standard form.
Where (x1, y1) and
(x2, y2) are two points
on the line such that

10. Two – Point Form
)(
)(
)(
1
12
12
1 xx
xx
yy
yy 



Where (x1, y1) and
(x2, y2) are two points
on the line such that
21 xx 
3. Write an equation of the line passing through
the points (-1, -2) and (6, 8). Express your
answer in standard form.

11. Two – Point Form
)(
)(
)(
1
12
12
1 xx
xx
yy
yy 



Where (x1, y1) and
(x2, y2) are two points
on the line such that
21 xx 
4. Write an equation of the line passing through
the points (-1, -2) and (6, 8). Express your
answer in standard form.

12. Intercepts Form
where a and b are not equal to 0, and a and b are
the x- and y-intercepts of the line, respectively.
1
b
y
a
x
1. Write an equation of the line with 2 as x-
intercept and 6 as y-intercept. Express your
answer in standard form.

13. Intercepts Form
where a and b are not equal to 0, and a and b are
the x- and y-intercepts of the line, respectively.
1
b
y
a
x
2. Write an equation of the line with 3 as x-
intercept and 5 as y-intercept. Express your
answer in standard form.

14. Intercepts Form
where a and b are not equal to 0, and a and b are
the x- and y-intercepts of the line, respectively.
1
b
y
a
x
3. Write an equation of the line with 1 as x-
intercept and 4 as y-intercept. Express your
answer in standard form.

15. Take the Challenge
1. Find the equation in standard form of the line
passing through (0, -2) and whose slope is 2/3.
2. Find the equation of the line that passes
through (2, 5) and with slope 6. Write the
equation in standard form and slope-intercept
form.
3. Find the equation of the line that contains the
point (2, -1) and perpendicular to y – 3x = 6.

16. Application
You are one of the scientists excavating for
dinosaur remains. To guide your team, you
decided to map the excavation site on a
rectangular coordinate system. One of the bones
lies from (-5, 8) to (10, -1) and another bone lies
from (-10, -3) to (-5, -6). Previous excavations
indicate that the bones excavated are parallel to
each other. The excavation team leader wants to
find out if the positions of the bones are parallel.
a. Find the equations in standard form.
b. Prove if the bones are parallel to each other.