Lesson 6-5 Point-Slope Form And Writing Linear Equations Worksheet With Answers
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2
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4
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6Point-Slope Form and
6-5
6-5
6-5
6-5
Writing Linear Equations
1. Plan
Objectives
What You’ll Learn
GO
for Help
Check Skills You’ll Need
Lessons 6-1 and 2-4
1
To graph and write linear
•
To graph and write linear
equations using point-slope
Find the rate of change of the data in each table.
equations using point-slope
form
1
–2
form
1.
2.
3.
2
x
y
x
y
x
y
2
2
To write a linear equation
•
To write a linear equation
2
4
3
5
10
4
using data
using data
5
2
1
4
7.5
1
Examples
. . . And Why
8
8
1
3
5
6
1
Graphing Using Point-Slope
11
14
3
2
2.5
11
To write an equation relating
Form
altitude and the boiling point
2
Writing an Equation in
of water, as in Example 5
Simplify each expression.
Point-Slope Form
4
4. -3(x - 5)
–3x ± 15
5. 5(x + 2)
5x ± 10
2
(x 2 6)
6.
3
Using Two Points to Write
9
8
– x ±
4
an Equation
New Vocabulary •
9
3
point-slope form
4
Writing an Equation Using
a Table
5
Real-World Problem Solving
6
1 1
Using Point-Slope Form
Part 1
Point-Slope Form
Math Background
You can use the definition of slope to find another form of a linear equation called
No matter what form a linear
the point-slope form.
equation is written in, the
y
2 y
2
1
coordinates of every point on the
= m
Use the definition of slope.
x
2 x
2
1
graph of the line satisfy its linear
equation and, conversely, every
Suppose you know that a line passes through the point (3, 4) and has slope 2.
pair of values that satisfy the
y 2 4
equation represent a point on
Substitute (3, 4) for (x
, y
) and substitute (x, y) for (x
, y
).
= 2
1
1
2
2
x 2 3
the graph.
Substitute 2 for m.
y 2 4
(x - 3)
=
2(x - 3)
Multiply each side by x – 3.
More Math Background:
p. 306D
x 2 3
y - 4 = 2(x - 3)
Simplify the left side of the equation.
Lesson Planning and
The equation y - 4 = 2(x - 3) is in point-slope form.
Resources
y -
= 2(x - 3)
4
See p. 306E for a list of the
Q
c
a
resources that support this lesson.
y-coordinate
slope
x-coordinate
PowerPoint
Bell Ringer Practice
Key Concepts
Definition
Point-Slope Form of a Linear Equation
Check Skills You’ll Need
The
point-slope form
of the equation of a nonvertical line that passes
For intervention, direct students to:
through the point (x
, y
) and has slope m is
1
1
y -
= m(x -
Rate of Change and Slope
y
x
)
1
1
Lesson 6-1: Example 1
Extra Skills and Word
Problem Practice, Ch. 6
336
Chapter 6
Linear Equations and Their Graphs
The Distributive Property
Lesson 2-4: Example 3
Extra Skills and Word
Special Needs
L1
Below Level
L2
Problem Practice, Ch. 2
In Example 2, to help any confusion about the signs,
In Step 2 of Example 4, have students write equations
students graph a line and label two points. Then they
in point-slope form using each ordered pair in the
write an equation for slope using the coordinates of
table. Then ask them to show that all four equations
the points. Ask: What operation do you use to find
are equivalent.
the rise or the run?
subtraction
learning style: verbal
learning style: verbal
336
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