Point-Slope Formula Worksheets With Answer Key - Section 3.5 - 3.6
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Section 3.5 Point-Slope Formula
Point-Slope Formula
Section 3.5
1. Writing an Equation of a Line Using
Concepts
the Point-Slope Formula
1. Writing an Equation of a
Line Using the Point-Slope
In Section 3.4, the slope-intercept form of a line was used as a tool to construct an
Formula
equation of a line. Another useful tool to determine an equation of a line is the
2. Writing an Equation of a
point-slope formula. The point-slope formula can be derived from the slope for-
Line Given Two Points
mula as follows:
1x
2
1x, y2
3. Writing an Equation of
, y
and has slope m. If
Suppose a line passes through a given point
is
1
1
a Line Parallel or
any other point on the line, then:
Perpendicular to Another
Line
y
y
1
m
Slope formula
4. Different Forms of Linear
x
x
1
Equations: A Summary
2
1x
2
y
y
1
m1x
x
x
Clear fractions.
1
1
x
x
1
2
m1x
x
y
y
1
1
2
y
y
m1x
x
Point-slope formula
1
1
FORMULA Point-Slope Formula
The point-slope formula is given by
2
y
y
m1x
x
1
1
1x
2
where m is the slope of the line and
, y
is a known point on the line.
1
1
Example 1 demonstrates how to use the point-slope formula to find an equation of
a line when a point on the line and slope are given.
Writing an Equation of a Line Using
Example 1
the Point-Slope Formula
Use the point-slope formula to write an equation of the line having a slope of 3
1 2,
and passing through the point
42.
Write the answer in slope-intercept form.
Solution:
The slope of the line is given:
m
3
1x
2
1 2,
A point on the line is given:
, y
42
1
1
The point-slope formula:
2
y
y
m1x
x
1
1
1 42
1 22 4
y
33x
Substitute
m
3, x
2, and y
4.
1
1
y
4
31x
22
Simplify. Because the final answer is required in
slope-intercept form, simplify the equation and
solve for y.
y
4
3x
6
Apply the distributive property.
y
3x
2
Slope-intercept form
Skill Practice
1. Use the point-slope formula to write an equation of the line having a slope
Answer
of
4 and passing through ( 1, 5). Write the answer in slope-intercept form.
1. y
4x
1
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