CCSS SENSE-MAKING AND PERSEVERANCE Graph each set of

All three lines cross the y-axis at the same point.
Extend 4-1: Graphing Technology Lab The Family of Linear Graphs
They have the same y-intercept, but different slopes.
CCSS SENSE-MAKING AND
PERSEVERANCE Graph each set of equations
on the same screen. Describe the similarities
or differences.
1. y = 2x
y = 2x + 3
y = 2x − 7
SOLUTION: Enter each equation into the graphing calculator at Y
= list and then graph.
3. y = x + 4
y = 2x + 4
y=
x+4
SOLUTION: Enter each equation into the graphing calculator at Y
= list and then graph.
All three lines cross the y-axis at the same point.
They have the same y-intercept, but different slopes.
All three lines are parallel. They have the same
slope, but different intercepts.
2. y = x + 1
y = 2x + 1
y=
x+1
4. y = 0.5x + 2
y = 0.5x − 5
y = 0.5x + 4
SOLUTION: Enter each equation into the graphing calculator at Y
= list and then graph.
SOLUTION: Enter each equation into the graphing calculator at Y
= list and then graph.
All three lines are parallel. They have the same
slope, but different y-intercepts.
All three lines cross the y-axis at the same point.
They have the same y-intercept, but different slopes.
3. y = x + 4
y = 2x + 4
y=
x+4
5. y = −2x − 2
y = −4x − 2
y =− x−2
SOLUTION: Enter each equation into the graphing calculator at Y
= list and then graph.
SOLUTION: Enter each equation into the graphing calculator at Y
= list and then graph.
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Page 1
mx + b have in common?
SOLUTION: All three
lines are parallel.
They have
the same
Graphs that are in the form y = mx + b are all
Extend
4-1: Graphing
Technology
Lab The
Family of Linear Graphs
slope, but different y-intercepts.
nonvertical lines.
5. y = −2x − 2
y = −4x − 2
y =− x−2
SOLUTION: Enter each equation into the graphing calculator at Y
= list and then graph.
8. How does the value of b affect the graph of y = mx
+ b?
SOLUTION: The value of b determines the y-intercept. It is the
point where the line crosses the y-axis. Lines with
positive y-intercept’s cross the y-axis above the xaxis, while lines with negative y-intercept’s cross the
y-axis below the x-axis. When b is zero, the line
crosses the axis at the origin. 9. What is the result of changing the value of m on the
graph of y = mx + b if m is positive?
All three lines cross the y-axis at the same point.
They have the same y-intercept, but different slopes.
SOLUTION: Changing the value of m changes the slope of the
graph. If m is positive, then the greater the value of m
the steeper the graph. For example, the graph of y = 6x + 2 is steeper than
the graph of y = 2x + 2.
6. y = 3x
y = 3x + 6
y = 3x − 7
SOLUTION: Enter each equation into the graphing calculator at Y
= list and then graph.
[–5, 10] scl: 1 by [–5, 10] scl: 1
10. How can you determine which graph is steepest by
examining the following equations?
y = 3x, y = −4x − 7,
All three lines are parallel. They have the same
slope, but different y-intercepts.
7. Families of graphs have common characteristics.
What do the graphs of all equations of the form y =
mx + b have in common?
SOLUTION: Determine which graph that has the absolute value of
m the greatest. The graph of y = −4x − 7 is steepest
because the absolute value of m is 4 compared to 3
and .
SOLUTION: Graphs that are in the form y = mx + b are all
nonvertical lines.
8. How does the value of b affect the graph of y = mx
+ b?
SOLUTION: The value of b determines the y-intercept. It is the
point where the line crosses the y-axis. Lines with
positive y-intercept’s cross the y-axis above the xeSolutions Manual - Powered by Cognero
axis, while lines with negative y-intercept’s cross the
y-axis below the x-axis. When b is zero, the line
crosses the axis at the origin. [−10, 10] scl: 1 by [−10, 10] scl: 1
11. Explain how knowing about the effects of m and b
can help you sketch the graph of an equation.
Page 2
SOLUTION: The value of m tells you how steep the graph should
Extend 4-1: Graphing Technology Lab The Family of Linear Graphs
[−10, 10] scl: 1 by [−10, 10] scl: 1
11. Explain how knowing about the effects of m and b
can help you sketch the graph of an equation.
SOLUTION: The value of m tells you how steep the graph should
be compared to the graph of y = x and the value of b
tells you how many units higher or lower than
the graph will be. Graph the equation by first plotting the y-intercept (b), then use the slope (m) to
plot the next point. Draw a line through the points. 14. y = x
2
2
y =x +3
2
y = (x − 2)
SOLUTION: The widths of each graph are the same and they all
open up. However, each graph has different yintercepts.
12. The equation y = k can also be a parent graph.
Graph y = 5, y = 2, and y = −4 on the same screen.
Describe the similarities or differences among the
graphs.
SOLUTION: The graphs are all horizontal lines. They are all
parallel. They intersect the y-axis at different points.
2
15. y = x
2
y = 2x + 4
2
y = (3x) − 5
SOLUTION: All the graph open up. However, the graphs have
different widths and different y-intercepts.
Extension
Nonlinear functions can also be defined in terms
of a family of graphs. Graph each set of
equations on the same screen. Describe the
similarities or differences.
2
13. y = x
2
y = −3x
y = (−3x)
2
SOLUTION: All of the graphs intersect the y-axis at the same
point. This means that the graphs have the same yintercept. However, the graph have different widths
and two open up and one opens down. 14. y = x
16. Describe the similarities and differences in the
2
2
classes of functions f (x) = x + c and f (x) = (x + c) ,
where c is any real number.
SOLUTION: 2
In the graph of f (x) = x + c, the graph is the like f (x)
2
= x , but shifted vertically units. 2
In the graph of f (x) = (x + c) , the graph is the like f
2
(x) = x , but shifted horizontally units.
When the c is inside the parenthesis, the graph is
shifted horizontally, when it is outside, it is shifted
vertically units
. 2
2
y =x +3
2
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SOLUTION: Page 3

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