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11-4
11-4Point-Slope
Point-SlopeForm
Form
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
Pre-Algebra
11-4 Point-Slope Form
HOMEWORK answers
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Pre-Algebra
11-4 Point-Slope Form
Pre-Algebra HOMEWORK
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Pre-Algebra
11-4 Point-Slope Form
Our Learning Goal
Students will be able to graph
lines using linear equations,
understand the slope of a line
and graph inequalities.
Pre-Algebra
11-4 Point-Slope Form
Our Learning Goal Assignments
• Learn to identify and graph linear equations.
• Learn to find the slope of a line and use slope to understand
and draw graphs.
• Learn to use slopes and intercepts to graph linear equations.
• Learn to find the equation of a line given one point and the
slope.
• Learn to recognize direct variation by graphing tables of data
and checking for constant ratios.
• Learn to graph inequalities on the coordinate plane.
• Learn to recognize relationships in data and find the equation
of a line of best fit.
Pre-Algebra
11-4 Point-Slope Form
Today’s Learning Goal Assignment
Learn to find the
equation of a line
given one point
and the slope.
Pre-Algebra
11-4 Point-Slope Form
Vocabulary
point-slope form
Pre-Algebra
11-4 Point-Slope Form
The point-slope of an equation of a line
with slope m passing through (x1, y1) is
y – y1 = m(x – x1).
Point on the line
(x1, y1)
Point-slope form
y – y1 = m (x – x1)
slope
Pre-Algebra
11-4 Point-Slope Form
Additional Example 1: 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.
A. y – 7 = 3(x – 4)
y – y1 = m(x – x1)
The equation is in point-slope
y – 7 = 3(x – 4) form.
Read the value of m from the
m=3
equation.
(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).
Pre-Algebra
11-4 Point-Slope Form
Additional Example 1B: Using Point-Slope Form to
Identify Information About a Line
B. y – 1 = 1 (x + 6)
3
y – y1 = m(x – x1)
y – 1 = 1 (x + 6)
3
1
Rewrite using subtraction
y – 1 = 3 [x – (–6)]
instead of addition.
m =1
3
(x1, y1) = (–6, 1)
The line defined by y – 1 = 1 (x + 6) has slope 1 , and
3
3
passes through the point (–6, 1).
Pre-Algebra
11-4 Point-Slope Form
Try This: Example 1
Use the point-slope form of each equation to
identify a point the line passes through and
the slope of the line.
A. y – 5 = 2 (x – 2)
y – y1 = m(x – x1)
y – 5 = 2(x – 2) The equation is in point-slope
form.
Read the value of m from the
m=2
equation.
(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).
Pre-Algebra
11-4 Point-Slope Form
Try This: Example 1B
B. y – 2 = 2 (x + 3)
3
y – y1 = m(x – x1)
y – 2 = 2 (x + 3)
3
Rewrite using subtraction
y – 2 =2
[x
–
(–3)]
3
instead of addition.
m =2
3
(x1, y1) = (–3, 2)
The line defined by y – 2 = 2 (x + 3) has slope 2 , and
3
3
passes through the point (–3, 2).
Pre-Algebra
11-4 Point-Slope Form
Additional Example 2: 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.
A. the line with slope 4 passing through (5, -2)
y – y1 = m(x – x1)
[y – (–2)] = 4(x – 5)
y + 2 = 4(x – 5)
Substitute 5 for x1, –2 for y1,
and 4 for m.
The equation of the line with slope 4 that passes through
(5, –2) in point-slope form is y + 2 = 4(x – 5).
Pre-Algebra
11-4 Point-Slope Form
Try This: Example 2A
Write the point-slope form of the equation with
the given slope that passes through the indicated
point.
A. the line with slope 2 passing through (2, –2)
y – y1 = m(x – x1)
[y – (–2)] = 2(x – 2)
y + 2 = 2(x – 2)
Substitute 2 for x1, –2 for y1,
and 2 for m.
The equation of the line with slope 2 that passes through
(2, –2) in point-slope form is y + 2 = 2(x – 2).
Pre-Algebra
11-4 Point-Slope Form
Additional Example 2: Writing the Point-Slope Form
of an Equation
B. the line with slope –5 passing through (–3, 7)
y – y1 = m(x – x1)
y – 7 = -5[x – (–3)] Substitute –3 for x1, 7 for y1,
and –5 for m.
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).
Pre-Algebra
11-4 Point-Slope Form
Try This: Example 2B
B. the line with slope -4 passing through (-2, 5)
y – y1 = m(x – x1)
y – 5 = –4[x – (–2)] Substitute –2 for x1, 5 for y1,
and –4 for m.
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).
Pre-Algebra
11-4 Point-Slope Form
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.
As x increases by 30, y increases by 20, so the slope
2
of the line is 20 or . The line passes through the
30
3
point (0, 18).
Pre-Algebra
11-4 Point-Slope Form
Additional Example 3 Continued
y – y1 = m(x – x1)
Substitute 0 for x1, 18 for y1,
y – 18 = 2
3 (x – 0)
and 2 for m.
3
The equation of the line the roller coaster travels along,
in point-slope form, is y – 18 = 2 x. Substitute 150 for x
3
to find the value of y.
y – 18 = 2
3 (150)
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.
Pre-Algebra
11-4 Point-Slope Form
Try This: 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.
As x increases by 45, y increases by 15, so the slope
1
of the line is 15 or . The line passes through the
45
3
point (0, 15).
Pre-Algebra
11-4 Point-Slope Form
Try This: Example 3 Continued
y – y1 = m(x – x1)
Substitute 0 for x1, 15 for y1,
y – 15 = 1
3 (x – 0)
and 1 for m.
3
The equation of the line the roller coaster travels along,
in point-slope form, is y – 15 = 1 x. Substitute 300 for x
3
to find the value of y.
y – 15 = 1
3 (300)
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.
Pre-Algebra
11-4 Point-Slope Form
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) (–5, –6), 2
2
2. y – 4 = – 2 (x – 6) (6, 4), – 5
5
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)
y – 5 = 4(x – 3)
4. the line with slope –2 passing through (–2, 4)
y – 4 = –2(x + 2)
Pre-Algebra