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Graph . Equations of Lines. Objectives:. To find the slope of a line given 2 points. To classify a line based on its slope. To find the slope of parallel and perpendicular lines. To graph the equation of a line using slope-intercept and standard form of a line. ID: 732308

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## Presentations text content in Find Slope & Rate of Change

Find Slope & Rate of ChangeGraph Equations of Lines

Objectives:

To find the slope of a line given 2 points

To classify a line based on its slope

To find the slope of parallel and perpendicular lines

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

Slide2Vocabulary

Slope

Rate

of Change

Parallel

Perpendicular

Parent

Function

Intercepts

Slope-Intercept

Form

Standard Form

Slide3Objective 1

You will be able to find the slope between two points

Slide4Slope

Anything that isn’t completely vertical has a slope. This is a value used to describe its incline or decline.

Slide5Rate 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 1Describe some real-world rates of change.

Slide7Practical 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?

Slide8Pitch 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.

Slide9Slope Definition

The

slope

m

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

Slide10Exercise 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?

Slide11Exercise 3Find the slope of the line passing through the points (

−

4,

−

5) and (6,

−2).

Slide12Exercise 4Find the value of

k

such that the line passing through the points (

−

4, 2

k) and (k, −5) has slope −1.

Slide13Objective 2

You will be able use slope to be

able to tell what kind of

line you have

Slide14The 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

Insert

Picture

Insert

Picture

Insert

Picture

Insert

Picture

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

the line gets steeper.

Slide15Exercise 5Without graphing, tell whether the line through the given points rises, falls, is horizontal, or is vertical.

(1, 6); (8,

−

1)

(

−4, −3); (7, 1)(−5, 3); (−5, 1)(9, 2); (−9, 2)

Slide16Objective 3

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

Slide17Parallel 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.

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.

Slide19Exercise 6 Tell whether the pair of lines are parallel, perpendicular, or neither

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

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

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

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

Slide20Exercise 7

If two distinct lines are parallel, what do you know about their

y

-intercepts?

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?

Slide21Objective 4

You will be able to graph the equation of a line in slope- intercept or standard form

Slide22Parent FunctionsWho 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 FunctionsLinear Parent Function

Family of Linear Functions

Linear Parent

Function

Slide23Parent FunctionsWho 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 FunctionsQuadratic Parent Function

Family of

Quadratic

Functions

Quadratic

Parent

Function

Slide24Parent FunctionsWho 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 FunctionsParent FunctionA group of functions that share common characteristicsSimplest member of the family

Slide25Parent Functions

Linear parent function:

or

All other linear functions can be formed with transformations on the parent function.

Slide26Intercepts

Click me!

The

-intercept

of a graph is where it intersects the

-axis.

The

-intercept

of a graph is where it intersects the

-axis.

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 8aWithout your graphing calculator, graph each of the following:

Exercise 8bWithout your graphing calculator, graph each of the following:

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

Slide32Standard FormTo graph an equation in standard form:

Write equation in standard form.

Let

x

= 0 and solve for

y. This is your y-intercept.Let y = 0 and solve for x. This is your x-intercept.Connect the dots.

Slide333.

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 9aWithout your graphing calculator, graph each of the following:

Exercise 9bWithout your graphing calculator, graph each of the following:

Exercise 10For an equation in standard form,

A

x

+

B

y = C, what is the slope of the line in terms of A and B?

Slide37Horizontal and Vertical Lines

Horizontal

Line

The

graph of

is a horizontal line through . Vertical LineThe graph of

is a

vertical

line

through

.

Exercise 11Graph each of the following

:

Find Slope & Rate of ChangeGraph Equations of Lines

Objectives:

To find the slope of a line given 2 points

To classify a line based on its slope

To find the slope of parallel and perpendicular lines

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

Slide40Slide41