slope advanced

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Slope-Intercept Form

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Warm Up

Solve each problem.

1. Graph the following ordered pairs on a coordinate

plane: (1, 1), (−4, 2), and (−1, −1).

McGraw Hill | Slope-Intercept Form

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Warm Up

2. Find the slope of the line that passes through (−4, −3)

and (10, 6).

3. Explain why y = 3x + 4 does not represent a

proportional relationship.

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Warm Up

Solve each problem.

1. Graph the following ordered pairs on a coordinate

plane: (1, 1), (−4, 2), and (−1, −1).

McGraw Hill | Slope-Intercept Form

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Warm Up

McGraw Hill | Slope-Intercept Form

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Florida’s B.E.S.T. Standards for
Mathematics

MA.8.AR.3.3 Given a table, graph or written description
of a linear relationship, write an equation in
slope-intercept form.

MA.8.AR.3.5 Given a real-world context, determine and
interpret the slope and y-intercept of a two-variable linear
equation from a written description, a table, a graph or
an equation in slope-intercept form.

McGraw Hill | Slope-Intercept Form

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Florida’s Mathematical Thinking and
Reasoning Standards

MA.K12.MTR.1.1
Actively participate in effortful learning both individually and
collectively.

MA.K12.MTR.4.1
Engage in discussions that reflect on the mathematical thinking
of self and others.

MA.K12.MTR.5.1
Use patterns and structure to help understand and connect
mathematical concepts.

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Florida’s Mathematical Thinking and
Reasoning Standards

MA.K12.MTR.7.1
Apply mathematics to real-world contexts.

McGraw Hill | Slope-Intercept Form

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Lesson Objectives

Content Objective
Students will write linear relationships in the form y = mx + b.

Language Objective
Students will explain what the y-intercept and the slope
represent in the context of a real-world problem.

McGraw Hill | Slope-Intercept Form

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Learn
Slope-Intercept Form of a Line

Nonproportional linear relationships can
be written in the form y = mx + b. This is
called the slope-intercept form.

When an equation is written in this form, m is the slope and b
is the y-intercept. The y-interceptof a line is the y-coordinate
of the point where the line crosses the y-axis.

McGraw Hill | Slope-Intercept Form

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Learn
Slope-Intercept Form of a Line

Equation

Graph

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Learn
Slope-Intercept Form of a Line

In a nonproportional linear relationship, the
graph passes through the point (0, b), which
is the y-intercept.

You can use the slope formula to derive the
equation of a line in slope-intercept form.

McGraw Hill | Slope-Intercept Form

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Learn
Slope-Intercept Form of a Line

Slope formula

(x1, y1) = (0, b); (x2, y2) = (x, y)

Simplify.

y − b = m · x

Multiplication Property of Equality

y = mx + b

Addition Property of Equality

McGraw Hill | Slope-Intercept Form

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Learn
Slope-Intercept Form of a Line

Think About It!

How will using the slope-intercept form of a linear
equation help identify the slope and y-intercept?

McGraw Hill | Slope-Intercept Form

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Example 1
Identify Slopes and y-Intercepts

Identify the slope and y-intercept of the graph of the
equation

McGraw Hill | Slope-Intercept Form

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Example 1
Identify Slopes and y-Intercepts

To identify the slope and y-intercept of the equation, write
the equation in the form y = mx + b.

Write the equation in the form y = mx + b.

y = mx + b

McGraw Hill | Slope-Intercept Form

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Example 1
Identify Slopes and y-Intercepts

McGraw Hill | Slope-Intercept Form

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Example 1
Identify Slopes and y-Intercepts

McGraw Hill | Slope-Intercept Form

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only and may not be further reproduced or distributed.

Example 1
Identify Slopes and y-Intercepts

McGraw Hill | Slope-Intercept Form

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Example 2
Write Equations in Slope-Intercept Form

Write the equation of a line in slope-intercept form
with a slope of −3 and a y-intercept of −4.

McGraw Hill | Slope-Intercept Form

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Example 2
Write Equations in Slope-Intercept Form

Slope-intercept form.

y = −3x + (−4)Replace m with −3 and b with −4.

y = −3x − 4

Simplify.

So, the equation of the line is y = −3x − 4.

McGraw Hill | Slope-Intercept Form

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Example 2
Write Equations in Slope-Intercept Form

Check

Write the equation of a line in slope-intercept
form with a slope of 5 and a y-intercept of −7.

McGraw Hill | Slope-Intercept Form

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Example 2
Write Equations in Slope-Intercept Form

Check

Write the equation of a line in slope-intercept
form with a slope of 5 and a y-intercept of −7.

y = 5x − 7

McGraw Hill | Slope-Intercept Form

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Learn
Write Equations in Slope-Intercept
Form From Graphs

You can write an equation in slope-intercept
form of a nonproportional linear relationship
from its graph using these steps.

1. Find the location where the line crosses

the y-axis to determine the y-intercept.

2. Find the ratio of rise to run to determine

the slope.

3. Substitute the values for slope, m, and

y-intercept, b, in the equation y = mx + b.

McGraw Hill | Slope-Intercept Form

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Example 3
Write Equations in Slope-Intercept Form

Write an equation in slope-intercept form
for the graph shown.

McGraw Hill | Slope-Intercept Form

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Example 3
Write Equations in Slope-Intercept Form

Step 1Find the y-intercept.

The line crosses the y-axis at (0, 4). So, the
y-intercept is 4.

McGraw Hill | Slope-Intercept Form

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Example 3
Write Equations in Slope-Intercept Form

McGraw Hill | Slope-Intercept Form

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Example 3
Write Equations in Slope-Intercept Form

Step 3Write the equation.

Substitute the values for slope, m, and y-intercept, b,
in the equation y = mx + b .

y = mx + b

Slope-intercept form

McGraw Hill | Slope-Intercept Form

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Example 3
Write Equations in Slope-Intercept Form

Check

Write an equation in slope-intercept form
for the graph shown.

McGraw Hill | Slope-Intercept Form

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Example 3
Write Equations in Slope-Intercept Form

Check

Write an equation in slope-intercept form
for the graph shown.

y = −3x + 2

McGraw Hill | Slope-Intercept Form

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Learn
Write Equations in Slope-Intercept
Form From Verbal Descriptions

When an equation in slope-intercept form applies to a
real-world situation, the slope represents the rate of
change and the y-intercept represents the initial value.

You can write an equation in slope-intercept form given
the following real-world situation.

Bamboo is one of the fastest growing plants on Earth.
Suppose a bamboo seedling is 5 centimeters tall and
grows at a rate of 6.5 centimeters a day.

McGraw Hill | Slope-Intercept Form

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Learn
Write Equations in Slope-Intercept
Form From Verbal Descriptions

McGraw Hill | Slope-Intercept Form

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Learn
Write Equations in Slope-Intercept
Form From Verbal Descriptions

Step 2Write the equation in slope-intercept

form y = mx + b.

y = 6.5x + 5

McGraw Hill | Slope-Intercept Form

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Example 4
Write Equations in Slope-Intercept Form

Student Council is selling T-shirts during spirit week. It
costs $20 for the design and $5 to print each shirt.

Write an equation in slope-intercept form to represent
the total cost y for printing any number of shirts x.

McGraw Hill | Slope-Intercept Form

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Example 4
Write Equations in Slope-Intercept Form

Step 1Find the slope and y-intercept.

The slope represents the rate of change or cost per T-shirt.
It costs $5 to print each shirt.

The y-intercept represents the initial cost of the design. The
one-time charge for the design is $20.

So, the slope is $5 and the y-intercept is $20.

McGraw Hill | Slope-Intercept Form

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Example 4
Write Equations in Slope-Intercept Form

Step 2Write the equation in slope-intercept

form y = mx + b.

So, the equation that represents the total cost of
printing any number of shirts is y = 5x + 20.

y = mx + b

Slope-intercept form

y = 5x + 20

Replace m with the rate of change, 5,
and b with the initial cost, 20.

McGraw Hill | Slope-Intercept Form

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Example 4
Write Equations in Slope-Intercept Form

Check

Faith is saving money in order to purchase a new
smartphone. She started out with $30 in her savings
account and is able to save an additional $15 a week.
Write an equation in slope-intercept form to represent
Faith’s total savings y for x weeks she puts money
toward the purchase of a new smartphone.

McGraw Hill | Slope-Intercept Form

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Example 4
Write Equations in Slope-Intercept Form

Check

Faith is saving money in order to purchase a new
smartphone. She started out with $30 in her savings
account and is able to save an additional $15 a week.
Write an equation in slope-intercept form to represent
Faith’s total savings y for x weeks she puts money
toward the purchase of a new smartphone.

y = 15x + 30

McGraw Hill | Slope-Intercept Form

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Learn
Write Equations in Slope-Intercept
Form From Tables

You can write an equation that represents
a nonproportional linear relationship in
slope intercept form from a table of
values.

First, determine the slope and y-intercept.
Then write the equation in the form
y = mx + b. The slope, or rate of change,
in the table is 6.

The y-intercept, or initial value, is 10. So,
the equation is y = 6x + 10.

McGraw Hill | Slope-Intercept Form

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Example 5
Write Equations in Slope-Intercept Form

Amanda is reading a novel for her Language Arts class.
The table shows the number of pages that Amanda has
left after a certain number of hours she spent reading.

Write an equation in slope-intercept form that
represents the data in the table.

Hours, x

0

2

4

6

8

Pages Left to
Read, y
360

280

200

120

40

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Example 5
Write Equations in Slope-Intercept Form

Step 1Find the slope.

As the hours increase by 2, the pages left to read
decrease by 80.

Definition of slope

Change in y = −80; change in x = 2

Simplify.

McGraw Hill | Slope-Intercept Form

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Example 5
Write Equations in Slope-Intercept Form

Talk About It!

What does the slope represent in the context of this
situation?

McGraw Hill | Slope-Intercept Form

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Example 5
Write Equations in Slope-Intercept Form

Step 2Find the y-intercept.

Find the y value when x is 0. When y is 360, x is 0, so the
y-intercept (or initial value) is 360.

McGraw Hill | Slope-Intercept Form

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Example 5
Write Equations in Slope-Intercept Form

So, the equation that represents the data is y = −40x + 360.

y = mx + b

Slope-intercept form

y = −40x + 360

Replace m with −40 and b with 36.

Step 3Write the equation.

Substitute the values for slope, m, and y-intercept, b, in
the equation.

McGraw Hill | Slope-Intercept Form

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Example 5
Write Equations in Slope-Intercept Form

Talk About It!

What does the y-intercept represent in the context of
this situation?

McGraw Hill | Slope-Intercept Form

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Example 5
Write Equations in Slope-Intercept Form

Check

The relationship between the data in the table is
linear. Write an equation in slope-intercept form
that represents the data in the table.

x

y

−1

6

0

3

1

0

2

−3

McGraw Hill | Slope-Intercept Form

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Example 5
Write Equations in Slope-Intercept Form

Check

The relationship between the data in the table is
linear. Write an equation in slope-intercept form
that represents the data in the table.

y = −3x + 3
x

y

−1

6

0

3

1

0

2

−3

McGraw Hill | Slope-Intercept Form

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Pause and Reflect

Did you struggle with writing equations in slope-intercept
form when the information was given in different forms,
such as graphs, words, or tables? If so, what can you do
to get help? If not, how could you explain the process to
another student?

McGraw Hill | Slope-Intercept Form

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Apply 5
Consumer Science

Amir wants to ship a birthday present to
his brother. Express Shipping charges a
$5 insurance fee to protect items that are
shipped and $0.50 for every ounce the
item weighs. Priority Postal’s shipping
costs are shown in the graph. The present
Amir wants to ship weighs 14.2 ounces.
Which company charges less to ship the
present? How much less?

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Apply 5
Consumer Science

Talk About It!

What does each slope and y-intercept represent in
the context of the problem?

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Apply 5
Consumer Science

Check
Katie wants to attend fitness classes at a local
gym. The costs of attending Fitness For Life are
represented in the graph shown.
Fitness World charges a registration fee of $90
plus $8 per month.
Katie wants a membership for 18 months. Which
gym charges less for 18 months? How much less?

McGraw Hill | Slope-Intercept Form

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Apply 5
Consumer Science

Check
Katie wants to attend fitness classes at a local
gym. The costs of attending Fitness For Life are
represented in the graph shown.
Fitness World charges a registration fee of $90
plus $8 per month.
Katie wants a membership for 18 months. Which
gym charges less for 18 months? How much less?

Fitness World; $26 less

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Exit Ticket

Suppose a sightseeing tour company charges $7.50
for each hour you rent a motorized scooter, plus a
non-refundable fee of $45. Write an equation that
represents the total cost, y, of renting the scooter in
relation to the number of hours, x.

McGraw Hill | Slope-Intercept Form

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Exit Ticket

Suppose a sightseeing tour company charges $7.50
for each hour you rent a motorized scooter, plus a
non-refundable fee of $45. Write an equation that
represents the total cost, y, of renting the scooter in
relation to the number of hours, x.

y = 7.50x + 45