Graphing Lines with a Table
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Example: Graph y = 2x - 1
Example: Graph y = 2x
Example: Graph 2x + 3y = 4
Ch 7 – Linear Equations
7.1 – Slope
Slope:
Example: Determine the slope of each line.
Rate of Change:
Example: The graph below shows the distance traveled by Rebecca and Ian during a day-long bicycle ride.
Find the slope of each line. To what does the slope refer?
Example: A line contains the points whose coordinates are listed in the table. Determine
the slope of the line.
Slope Formula:
Example: Determine the slope of each line.
The line through the points at (3, 8) and (3, 4)
The line through the points at (-4, 1) and (-3, -2)
The line through the points at (2, 5) and (3, 9)
The line through the points at (-8, 1) and (4, 1)
Types of Slope:
7.2 – Write Equations in Point-Slope Form
Point-Slope Form:
Example: Write the point-slope form of an equation for each line passing through the given point and
having the given point.
( 2, 7), m 
1
3
(4, 0), m  4
(3, 2), m  2
 5, 4  ,
m
2
3
Writing from a graph:
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Example: Write the point-slope form of an equation of the line below.
Example: Write the point-slope form of an equation for the line passing through (1, 4) and (3, -5)
Hints: find the slope first / it doesn’t matter which point you use.
7.3 – Writing Equations in Slope-Intercept Form
y-intercept:
x-intercept:
Slope-Intercept Form:
Example: Write an equation in slope-intercept form of each line with the given slope and y-intercept.
m = 3, b = -1
m = -2/3, b = 0
m = 0, b = -4
m = 2, b = 1
m = -5/3, b = 0
m = 0, b = -8
Example: Write an equation of the line in slope-intercept form for the situation
Slope 1 and passes through (2, 5)
Slope -3 and passes through (1, -4)
Passing through (-4, 4) and (2, 1)
Passing through (6, 2) and (3, -2)
Slope is ¾ and passes through (8, -2)
Passes through (2, 4) and (0, 5)
7.4 – Scatter Plots
Scatter Plot:
Types of Slope:
Examples: Determine whether the scatter plot shows a positive relationship, negative relationship, or no
relationship. If there is a relationship, describe it.
The scatter plot shows the number of years of experience and the salary for
each employee in a small company.
The scatter plot shows the word processing speeds of 12 students and the
number of weeks they have studied word processing.
7.5 – Graphing Linear Equations
Graphing with Intercepts:
Example: Determine the x-intercept and y-intercept of the graph of the line
2y – x = 8. Then graph.
Example: Determine the x-intercept and y-intercept of the graph of the line
3x – 2y = 12. Then graph.
Example: Determine the x-intercept and y-intercept of the graph of the line
x + y = 2. Then graph.
Example: Determine the x-intercept and y-intercept of the graph of the line 3x +
y = 3. Then graph.
Example: Determine the x-intercept and y-intercept of the graph of the line
4x – 5y = 20. Then graph.
Example: Suppose to ship a package it costs $2.05 for the first pound and $1.55 for each additional pound.
This can be represented by y = 2.05 + 1.55x. Determine the slope and y-intercept of the graph of the
equation.
Example: Determine the slope and y-intercept of the graph 6x – 9y = 18.
Example: Determine the slope and y-intercept of the graph of 4x + 3y = 6.
Example: Graph the following equations using slope intercept form.
y
2
x 5
3
1
y  x2
5
y
1
x3
2
3x  y  4
y  3
y  1
x4
x3
7.6 – Families of Linear Graphs
Review
Slope formula:
Point-Slope Form:
Slope-Intercept Form:
Linear Graphs:
Example: Graph the pair of equations. Describe any similarities or differences. Explain why they are a
family of graphs.
1
y  x2
2
1
y   1
2
y  5x 1
y  x 1
y  2x 1
y  2x  5
y  x 1
y  3x  1
Example: Gretchen and Max each have a savings account and plan to save $20 per month. The current
balance in Gretchen’s account is $150 and the balance in Max’s account is $100. Then y = 20x + 150 and
y = 20x + 100 represent how much money each has in their account, respectively, after x months. Compare
and contrast the graphs of the equations.
Parent Graphs:
Example: Change y = -3x – 1 so that the graph of the new equation fits each description.
Same y-intercept, less steep positive slope.
Same slope, y-intercept is shifted down 2 units.
Example: Change y = 2x + 1 so that the graph of the new equation fits each description.
Same slope, shifted down 1 unit
Same y-intercept, less steep positive slope
7.7 – Parallel and Perpendicular Lines
Parallel:
Parallel Lines:
Example: Determine whether the graphs of the equations are parallel.
y  3x  4
9 x  3 y  12
y  2x
7  2x  y
y  3 x  3
2 y  6x  5
Parallelogram:
Example: Determine whether figure EFGH is a parallelogram.
Example: Determine whether figure ABCD is a parallelogram.
Example: Write an equation in slope-intercept form of the line that is parallel to the graph y 
2
x  3 of and
3
passes through the point at (-3, 1).
Example: Write an equation in slope-intercept form of the line that is parallel to the graph y  6 x  4 of and
passes through the point at 2, 3).
Example: Write an equation in slope-intercept form of the line that is parallel to the graph 3x  2 y  9 of
and passes through the point at (2, 0).
Perpendicular Lines:
Example: Determine whether the graphs of the equations are perpendicular.
y  2 x  4
1
y  x3
2
1
x2
5
y  5x  1
y
y  4 x  3
4y  x 5
Example: Write an equation in slope-intercept form of the line that is perpendicular to the graph of
y  2 x  5 and passes through the point at (2, -3).
Example: Write an equation in slope-intercept form of the line that is perpendicular to the graph of
y  2 x  6 and passes through the point at (0, 0).
Example: Write an equation in slope-intercept form of the line that is perpendicular to the graph of
2 x  3 y  2 and passes through the point at (3, 0).