Find Slope & Rate of ChangeGraph Equations of Lines

Objectives:

1. To find the slope of a line given 2 points

2. To classify a line based on its slope

3. To find the slope of parallel and perpendicular lines

4. To graph the equation of a line using slope-intercept and standard form of a line

Vocabulary

Slope Rate of Change

Parallel Perpendicular

Parent Function Intercepts

Slope-Intercept Form Standard Form

Objective 1

You will

be able to fi

nd the

slope b

etween tw

o poin

ts

Slo

pe

Anything that isn’t com

pletely vertical

has a slope. This is a value used to

describe its incline or decline.

Rate of Change

Slope can be used to represent an average rate of change.

A rate of change is how much one quantity changes (on average) relative to another.

For slope, we measure how changes relative to .

Exercise 1

Describe some real-world rates of change.

Practical Slope

The slope or pitch of a roof is quite a useful measurement. How do you think a contractor would measure the slope or pitch of a roof?

Pitch of a Roof

The slope or pitch of a roof is defined as the number of vertical inches of rise for every 12 inches of horizontal run.

Slope Definition

The slope m of a nonvertical line is the ratio of vertical change (the ryse) to the horizontal change (the run).

ryse

ryse

Exercise 2

Regulations state that a handicap ramp must not exceed one inch of rise for every linear foot of run. If the maximum rise of a handicap ramp is 2.5 feet, what is the longest horizontal length of any handicap ramp?

Exercise 3

Find the slope of the line passing through the points (−4, −5) and (6, −2).

Exercise 4

Find the value of k such that the line passing through the points (−4, 2k) and (k, −5) has slope −1.

Objective 2You will be able use slope to be

able to tell what kind of

line you have

The Slope Game

The slope of a line indicates whether it rises or falls (L to R) or is horizontal or vertical.

m > 0 m < 0 m = 0 m = undef

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As the absolute value of the slope of a line increases, --?--.the line gets steeper.

Exercise 5

Without graphing, tell whether the line through the given points rises, falls, is horizontal, or is vertical.

1. (1, 6); (8, −1)

2. (−4, −3); (7, 1)

3. (−5, 3); (−5, 1)

4. (9, 2); (−9, 2)

Objective 3

You will be able to find the slopes of parallel and perpendicular lines

Parallel and Perpendicular

Two lines are parallel lines iff they are

coplanar and never intersect.

Two lines are perpendicular lines iff they intersect to form a right angle.

𝑚∥𝑛

Parallel and Perpendicular

Two lines are parallel lines iff they have the

same slope.

Two lines are perpendicular lines

iff their slopes are negative reciprocals.

Exercise 6

Tell whether the pair of lines are parallel, perpendicular, or neither

1. Line 1: through (-2, 1) and (0, -5)

Line 2: through (0, 1) and (-3, 10)

2. Line 1: through (-2, 2) and (0, -1)

Line 2: through (-4, -1) and (2, 3)

Exercise 7

1. If two distinct lines are parallel, what do you know about their y-intercepts?

2. If one of two perpendicular lines has a slope of 1/a and a < 0, is the slope of the other line positive or negative?

Obje

ctiv

e 4

You will

be able to graph th

e

equation of a

line in

slope-

intercept or s

tandard fo

rm

Parent Functions

Who is the simplest member of your family? Well, in math, the simplest member of a family of functions is called the parent function.

Family of Linear Functions Linear Parent Function

Parent Functions

Who is the simplest member of your family? Well, in math, the simplest member of a family of functions is called the parent function.

Family of Quadratic Functions Quadratic Parent Function

Parent Functions

Who is the simplest member of your family? Well, in math, the simplest member of a family of functions is called the parent function.

Family of Functions Parent Function

A group of functions that share common characteristics

Simplest member of the family

Parent Functions

Linear parent function: or

All other linear functions can be formed with

transformations on the parent function.

Intercepts

Click me!

6

4

2

-2

-5 5x-intercept

y-intercept

The -intercept of a graph is where it

intersects the -axis.

The -intercept of a graph is where it

intersects the -axis.

(𝑎 ,0 )

(0 ,𝑏 )

Slope-Intercept

Slope-Intercept Form of a Line:

If the graph of a line has slope and a -intercept of (0, ), then the equation of the line can be written in the form

Slope-intercept

4.

3.

2.

1.

Slope-Intercept

To graph an equation in slope-intercept form:

Draw line

Solve for

Use to plot

more points

Plot

Exercise 8a

Without your graphing calculator, graph each of the following:

1. 2.

Exercise 8b

Without your graphing calculator, graph each of the following:

3. 4.

Standard Form

Standard Form of a Line

The standard form of a linear

equation is , where and are not

both zero.Generally taken to be integers

Standard Form

To graph an equation in standard form:

1. Write equation in standard form.

2. Let x = 0 and solve for y. This is your y-intercept.

3. Let y = 0 and solve for x. This is your x-intercept.

4. Connect the dots.

3.2.1.

Standard Form

To graph an equation in standard form:

Let Let Draw line

Solve for Solve for

This is the -intercept

This is the -intercept

Exercise 9a

Without your graphing calculator, graph each of the following:

1. 2.

Exercise 9b

Without your graphing calculator, graph each of the following:

3. 4.

Exercise 10

For an equation in standard form, Ax + By = C, what is the slope of the line in terms of A and B?

Horizontal and Vertical Lines

Horizontal LineThe graph of is a

horizontal line through .

Vertical LineThe graph of is a

vertical line through .

6

4

2

-2

5

B: (0.00, 5.00)

A: (4.00, 0.00)

Exercise 11

Graph each of the following:1. 2.

Find Slope & Rate of ChangeGraph Equations of Lines

Objectives:

1. To find the slope of a line given 2 points

2. To classify a line based on its slope

3. To find the slope of parallel and perpendicular lines

4. To graph the equation of a line using slope-intercept and standard form of a line