Lesson 6-5 Point-Slope Form And Writing Linear Equations Worksheet With Answers Page 2
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5
62. Teach
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1
EXAMPLE
Graphing Using Point-Slope Form
EXAMPLE
1
Graph the equation y - 5 =
(x 2 2).
2
1.
y
Guided Instruction
y
2
6
The equation shows that the line passes
1
1
(4, 6)
.
through (2, 5) and has a slope .
2
2
(2, 5)
PowerPoint
Start at (2, 5). Using the slope, go up 1 unit
Additional Examples
and right 2 units to (4, 6). Draw a line through
2
x
O
2
the two points.
1
1
Graph the equation
x
O
2
4
1
y - 2 = (x - 1).
3
2
Quick Check
Graph the equation y - 5 =
2
(x 1 2).
1
1
y
See left.
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6
4
2
2
EXAMPLE
Writing an Equation in Point-Slope Form
EXAMPLE
2
Vocabulary Tip
Write the equation of the line that has slope -3 that passes through the
x
point (-1, 7).
Square brackets, [ ], are
O
2
2
4
6
grouping symbols
y - y
= m (x - x
)
Use the point-slope form.
2
1
1
commonly used when
y -
= -3[x - (-1)]
) and –3 for m.
parentheses, ( ), are
7
Substitute (–1, 7) for (x
, y
1
1
inside.
y - 7 = -3(x + 1)
Simplify inside the grouping symbols.
2
2
Write the equation of the line
with slope -2 that passes through
Quick Check
2
2
Write the equation of the line that has slope that passes through the point (10, -8).
2
5
the point (3, -3).
2
y 1 8 5
(x 2 10)
y ± 3 ≠ –2(x – 3)
5
If you know two points on a line, first use them to find the slope. Then you can
3
3
Write equations for the line in
write an equation using either point.
point-slope form and in slope-
intercept form.
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3
1
Using Two Points to Write an Equation
EXAMPLE
EXAMPLE
y – 4 ≠ – (x ± 1)
3
1
2
y ≠ – x ± 3
3
3
Write equations for the line in point-slope
y
y
form and in slope-intercept form.
(2, 3)
6
2
Step 1 Find the slope.
y
2 y
( 1, 4)
(2, 3)
x
4
2
O
2
4
2
1
= m
x
2 x
2
1
2
2
5 2 3
8
2
=
3
21 2 2
x
4
O
4
2
2
4
8
The slope is .
For: Point-Slope Activity
( 1,
5)
3
2
Use: Interactive Textbook, 6-5
Step 2 Use either point to write the
Step 3 Rewrite the equation
equation in point-slope form.
from Step 2 in slope-
intercept form.
Use (2, 3).
8
y - 3 =
(x 2 2)
y - y
= m(x - x
)
3
1
1
8
1
8
y - 3 = x -
5
(x 2 2)
y -
=
3
3
3
3
8
1
y = x -
2
3
3
Quick Check
3
3
a. Write an equation for the line in Example 3 in point-slope form using the
8
point (-1, -5).
y ± 5 ≠ (x ± 1)
3
y ≠ x – 2
8
1
b. Write the equation you found in part (a) in slope-intercept form.
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3
c. What is true about the equation you wrote in part (b) and the equation in Step 3
of Example 3?
They are the same.
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Lesson 6-5
Point-Slope Form and Writing Linear Equations
Advanced Learners
L4
English Language Learners
ELL
Have students write the slope-intercept form of the
Be sure that students understand that when a linear
linear equation found in Quick Check of Example 5.
equation is written in Point-Slope form, they can
Ask them what the y-intercept in the equation
identify a point on, and the slope of the graph of the
represents.
equation just by looking at the equation.
learning style: verbal
learning style: verbal
337
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