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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
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