Warm Up

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Warm Up
Problem of the Day
Lesson Presentation
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Warm Up Write the equation of the line that
passes through each pair of points in
slope-intercept form. 1. (0, 3) and (2, 3) 2.
(5, 3) and (5, 1) 3. (6, 0) and (0, 2) 4. (4,
6) and (2, 0)
y 3
x 5
y x 2
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Problem of the Day Without using equations for
horizontal or vertical lines, write the equations
of four lines that form a square.
Possible answer y x 2, y x 2, y x
2, y x 2
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Learn to find the equation of a line given one
point and the slope.
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Insert Lesson Title Here
Vocabulary
point-slope form
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The point-slope form of an equation of a line
with slope m passing through (x1, y1) is y y1
m(x x1).
Point on the line
Point-slope form
y y1 m (x x1)
(x1, y1)
slope
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Additional Example 1A Using Point-Slope Form to
Identify Information About a Line
Use the point-slope form of each equation to
identify a point the line passes through and the
slope of the line. y 7 3(x 4)
y y1 m(x x1)
The equation is in point-slope form.
y 7 3(x 4)
Read the value of m from the equation.
m 3
(x1, y1) (4, 7)
Read the point from the equation.
The line defined by y 7 3(x 4) has slope 3,
and passes through the point (4, 7).
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Additional Example 1B Using Point-Slope Form to
Identify Information About a Line
y 1 (x 6)
y y1 m(x x1)
Rewrite using subtraction instead of addition.
(x1, y1) (6, 1)
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Check It Out Example 1A
Use the point-slope form of each equation to
identify a point the line passes through and the
slope of the line. y 5 2 (x 2)
y y1 m(x x1)
The equation is in point-slope form.
y 5 2(x 2)
Read the value of m from the equation.
m 2
(x1, y1) (2, 5)
Read the point from the equation.
The line defined by y 5 2(x 2) has slope 2,
and passes through the point (2, 5).
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Check It Out Example 1B
y 2 (x 3)
y y1 m(x x1)
Rewrite using subtraction instead of addition.
(x1, y1) (3, 2)
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Additional Example 2A Writing the Point-Slope
Form of an Equation
Write the point-slope form of the equation with
the given slope that passes through the indicated
point. the line with slope 4 passing through (5,
2)
y y1 m(x x1)
Substitute 5 for x1, 2 for y1, and 4 for m.
y (2) 4(x 5)
y 2 4(x 5)
The equation of the line with slope 4 that passes
through (5, 2) in point-slope form is y 2
4(x 5).
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Additional Example 2B Writing the Point-Slope
Form of an Equation
the line with slope 5 passing through (3, 7)
y y1 m(x x1)
Substitute 3 for x1, 7 for y1, and 5 for m.
y 7 -5x (3)
y 7 5(x 3)
The equation of the line with slope 5 that
passes through (3, 7) in point-slope form is y
7 5(x 3).
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Check It Out Example 2A
Write the point-slope form of the equation with
the given slope that passes through the indicated
point. the line with slope 2 passing through (2,
2)
y y1 m(x x1)
Substitute 2 for x1, 2 for y1, and 2 for m.
y (2) 2(x 2)
y 2 2(x 2)
The equation of the line with slope 2 that passes
through (2, 2) in point-slope form is y 2
2(x 2).
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Check It Out Example 2B
the line with slope 4 passing through (2, 5)
y y1 m(x x1)
Substitute 2 for x1, 5 for y1, and 4 for m.
y 5 4x (2)
y 5 4(x 2)
The equation of the line with slope 4 that
passes through (2, 5) in point-slope form is y
5 4(x 2).
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Additional Example 3 Entertainment Application
A roller coaster starts by ascending 20 feet for
every 30 feet it moves forward. The coaster
starts at a point 18 feet above the ground. Write
the equation of the line that the roller coaster
travels along in point-slope form, and use it to
determine the height of the coaster after
traveling 150 feet forward. Assume that the
roller coaster travels in a straight line for the
first 150 feet.
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Additional Example 3 Continued
y y1 m(x x1)
y 18 100
y 118
The value of y is 118, so the roller coaster will
be at a height of 118 feet after traveling 150
feet forward.
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Check It Out Example 3
A roller coaster starts by ascending 15 feet for
every 45 feet it moves forward. The coaster
starts at a point 15 feet above the ground. Write
the equation of the line that the roller coaster
travels along in point-slope form, and use it to
determine the height of the coaster after
traveling 300 feet forward. Assume that the
roller coaster travels in a straight line for the
first 300 feet.
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Check It Out Example 3 Continued
y y1 m(x x1)
y 15 100
y 115
The value of y is 115, so the roller coaster will
be at a height of 115 feet after traveling 300
feet forward.
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Insert Lesson Title Here
Lesson Quiz
Use the point-slope form of each equation to
identify a point the line passes through and the
slope of the line. 1. y 6 2(x 5) 2. y
4 (x 6) Write the point-slope form of the
equation with the given slope that passes through
the indicated point. 3. the line with slope 4
passing through (3, 5) 4. the line with slope 2
passing through (2, 4)
(5, 6), 2
y 5 4(x 3)
y 4 2(x 2)