Five-Minute Check (over Lesson 4–2)
CCSS
Then/Now
New Vocabulary
Key Concept: Point-Slope Form
Example 1: Write and Graph an Equation in Point-Slope Form
Concept Summary: Writing Equations
Example 2: Writing an Equation in Standard Form
Example 3: Writing an Equation in Slope-Intercept Form
Example 4: Point-Slope Form and Standard Form
Over Lesson 4–2
Write an equation of the line that passes through
the given point and has the given slope.
(5, –7), m = 3
A. y = 22x + 3
B. y = 22x – 3
C. y = 3x + 22
D. y = 3x – 22
Over Lesson 4–2
Write an equation of the line that passes through
the given point and has the given slope.
(5, –7), m = 3
A. y = 22x + 3
B. y = 22x – 3
C. y = 3x + 22
D. y = 3x – 22
Over Lesson 4–2
Write an equation of the line that passes through
the given point and has the given slope.
(1, 5),
A.
B.
C.
D.
Over Lesson 4–2
Write an equation of the line that passes through
the given point and has the given slope.
(1, 5),
A.
B.
C.
D.
Over Lesson 4–2
Which equation is the line that passes through the
points (6, –3) and (12, –3)?
A. y = –3x + 1
B. y = –3x
C. y = –3
D. y = 3x
Over Lesson 4–2
Which equation is the line that passes through the
points (6, –3) and (12, –3)?
A. y = –3x + 1
B. y = –3x
C. y = –3
D. y = 3x
Over Lesson 4–2
Which equation is the line that passes through the
points (9, –4) and (3, –6)?
A. y = –3x – 7
B.
C.
D. y = x + 7
Over Lesson 4–2
Which equation is the line that passes through the
points (9, –4) and (3, –6)?
A. y = –3x – 7
B.
C.
D. y = x + 7
Over Lesson 4–2
Identify the equation for the line that has an
x-intercept of –2 and a y-intercept of 4.
A. y = –2x + 4
B. y = 2x + 4
C. y = 2x – 4
D. y = 4x – 2
Over Lesson 4–2
Identify the equation for the line that has an
x-intercept of –2 and a y-intercept of 4.
A. y = –2x + 4
B. y = 2x + 4
C. y = 2x – 4
D. y = 4x – 2
Over Lesson 4–2
Which is an equation of the
graph shown?
A.
B.
C. y = –2x + 3
D. y = 2x + 3
Over Lesson 4–2
Which is an equation of the
graph shown?
A.
B.
C. y = –2x + 3
D. y = 2x + 3
Content Standards
F.IF.2 Use function notation, evaluate functions for
inputs in their domains, and interpret statements that
use function notation in terms of a context.
F.LE.2 Construct linear and exponential functions,
including arithmetic and geometric sequences, given
a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table).
Mathematical Practices
2 Reason abstractly and quantitatively.
Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State
School Officers. All rights reserved.
You wrote linear equations given either one
point and the slope or two points.
• Write equations of lines in point-slope form.
• Write linear equations in different forms.
• point-slope form
Write and Graph an Equation in Point-Slope Form
Write the point-slope form of an equation for a line
that passes through (–2, 0) with slope
Point-slope form
(x1, y1) = (–2, 0)
Simplify.
Answer:
Write and Graph an Equation in Point-Slope Form
Write the point-slope form of an equation for a line
that passes through (–2, 0) with slope
Point-slope form
(x1, y1) = (–2, 0)
Simplify.
Answer:
Write and Graph an Equation in Point-Slope Form
Graph the equation
Plot the point at (–2, 0).
Use the slope to find another point on the line. Draw a
line through the two points.
Answer:
Write and Graph an Equation in Point-Slope Form
Graph the equation
Plot the point at (–2, 0).
Use the slope to find another point on the line. Draw a
line through the two points.
Answer:
Write the point-slope form of an
equation for a line that passes
through (4, –3) with a slope of –2.
A. y – 4 = –2(x + 3)
B. y + 3 = –2(x – 4)
C. y – 3 = –2(x – 4)
D. y + 4 = –2(x – 3)
Write the point-slope form of an
equation for a line that passes
through (4, –3) with a slope of –2.
A. y – 4 = –2(x + 3)
B. y + 3 = –2(x – 4)
C. y – 3 = –2(x – 4)
D. y + 4 = –2(x – 3)
Writing an Equation in Standard Form
In standard form, the variables are on the left side of
the equation. A, B, and C are all integers.
Original equation
Multiply each side by 4 to
eliminate the fraction.
Distributive Property
Writing an Equation in Standard Form
4y – 3x = 3x – 20 – 3x
–3x + 4y = –20
3x – 4y = 20
Answer:
Subtract 3x from each side.
Simplify.
Multiply each side by –1.
Writing an Equation in Standard Form
4y – 3x = 3x – 20 – 3x
–3x + 4y = –20
3x – 4y = 20
Subtract 3x from each side.
Simplify.
Multiply each side by –1.
Answer: The standard form of the equation is
3x – 4y = 20.
Write y – 3 = 2(x + 4) in standard form.
A. –2x + y = 5
B. –2x + y = 11
C. 2x – y = –11
D. 2x + y = 11
Write y – 3 = 2(x + 4) in standard form.
A. –2x + y = 5
B. –2x + y = 11
C. 2x – y = –11
D. 2x + y = 11
Writing an Equation in Slope-Intercept Form
Original equation
Distributive Property
Add 5 to each side.
Writing an Equation in Slope-Intercept Form
Simplify.
Answer:
Writing an Equation in Slope-Intercept Form
Simplify.
Answer: The slope-intercept form of the equation is
Write 3x + 2y = 6 in slope-intercept form.
A.
B. y = –3x + 6
C. y = –3x + 3
D. y = 2x + 3
Write 3x + 2y = 6 in slope-intercept form.
A.
B. y = –3x + 6
C. y = –3x + 3
D. y = 2x + 3
Point-Slope Form and Standard Form
A. GEOMETRY The figure shows trapezoid ABCD
with bases AB and CD.
Write an equation in___
point-slope form for the line
containing the side BC.
Point-Slope Form and Standard Form
Step 1 Find the slope of BC.
Slope formula
(x1, y1) = (4, 3) and
(x2, y2) = (6, –2)
Point-Slope Form and Standard Form
Step 2 You can use either point for (x1, y1) in the
point-slope form.
Using (4, 3)
Using (6, –2)
y – y1 = m(x – x1)
y – y1 = m(x – x1)
Point-Slope Form and Standard Form
Step 2 You can use either point for (x1, y1) in the
point-slope form.
Using (4, 3)
Using (6, –2)
y – y1 = m(x – x1)
y – y1 = m(x – x1)
Point-Slope Form and Standard Form
B. Write an equation in standard form for the same
line.
Original equation
Distributive Property
Add 3 to each side.
2y = –5x + 26
5x + 2y = 26
Answer:
Multiply each side by 2.
Add 5x to each side.
Point-Slope Form and Standard Form
B. Write an equation in standard form for the same
line.
Original equation
Distributive Property
Add 3 to each side.
2y = –5x + 26
5x + 2y = 26
Answer: 5x + 2y = 26
Multiply each side by 2.
Add 5x to each side.
A. The figure shows right triangle
ABC. Write the point-slope form of
the line containing the
hypotenuse AB.
A. y – 6 = 1(x – 4)
B. y – 1 = 1(x + 3)
C. y + 4 = 1(x + 6)
D. y – 4 = 1(x – 6)
A. The figure shows right triangle
ABC. Write the point-slope form of
the line containing the
hypotenuse AB.
A. y – 6 = 1(x – 4)
B. y – 1 = 1(x + 3)
C. y + 4 = 1(x + 6)
D. y – 4 = 1(x – 6)
B. The figure shows right triangle
ABC. Write the equation in standard
form of the line containing the
hypotenuse.
A. –x + y = 10
B. –x + y = 3
C. –x + y = –2
D. x – y = 2
B. The figure shows right triangle
ABC. Write the equation in standard
form of the line containing the
hypotenuse.
A. –x + y = 10
B. –x + y = 3
C. –x + y = –2
D. x – y = 2