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Chapter 5
Discovery 1
y-intercepts
Graph each linear equation and label the y-intercept.
1. y  x  5
2. y  x  5
3. y  x  10
4. y  x  10
Write a rule to determine the y-coordinate of the
y-intercept of a graph from its linear equation.
Chapter 5
Discovery 2
Linear Equations in Two Variables,
ax + by = c, where c = 0
Graph the following linear equations in two variables and
label the x-intercept and y-intercept:
1. x  y  0
2.  2 x  3 y  0
Write a rule for determining when the graph of an
equation has one point that is both the x-intercept
and y-intercept.
Chapter 5
Discovery 3
Types of Slopes
Determine the slopes of the following graphs:
1.
2.
7. In exercises 1 and 2, the linear function is increasing. The slopes have a
positive/negative value. Viewing the graphs from left to right, the graphs both
rise/fall.
11. In observing the absolute value of the slope, we see that the larger the absolute
value, the more/less steep is the graph.
1 of 3
Chapter 5
Discovery 3
Types of Slopes
Determine the slopes of the following graphs:
3.
4.
8. In exercises 3 and 4, the linear function is decreasing. The slopes have a
positive/negative value. Viewing the graphs from left to right, the graphs both rise/fall.
11. In observing the absolute value of the slope, we see that the larger the absolute
value, the more/less steep is the graph.
2 of 3
Chapter 5
Discovery 3
Types of Slopes
Determine the slopes of the following graphs:
5.
6.
9. In exercise 5, the linear function is constant. The slope is
0/undefined. The graph is a vertical/horizontal line.
10. In exercise 6, the graph does not represent a function. The slope is
0/undefined. The graph is a vertical/horizontal line.
3 of 3
Slope Formula
Chapter 5
Discovery 4
1. Locate and label the points ( 1, 3 ) and ( 5, 4 ) on a graph.
Draw a line connecting the points.
Draw the legs of a right triangle needed to determine the slope
of the line, and label each length.
2. The rise of the graph is _____.
3. The run of the graph is _____.
4. The difference of the y-coordinates of the ordered pair is
4 - 3 = _____.
5. The difference of the x-coordinates of the ordered pair is
5 - 1 = _____.
6. The slope of the graph is _____.
Write a rule to determine the slope of a graph from the coordinate of two
ordered pairs.
Chapter 5
Discovery 5
Determining Slope from a Linear Equation
1. Graph the given linear equations in two variables.
Label two integer coordinate points.
a. y  2 x  4
b. y  2 x
1
c. y  x  5
2
2. Determine the slope of each of the preceding lines.
3. Determine the coefficient of the x-term in each of the equations in
part 1.
Write a rule to determine the slope of the graph from a linear equation
in two variables.
Coinciding Lines
Chapter 5
Discovery 6
1. Graph the given pairs of linear equations.
a.  2 x  y  2 b. 2 x  4 y  4
c. 3 x  y  3
1
y  2x  2
y  x 1
y  3 x  3
2
2. Determine the slope and y-coordinate of the y-intercept for each graph.
a.  2 x  y  2 b. 2 x  4 y  4
c. y  3 x  5
1
y  2x  2
y  x 1
y  3 x  3
2
Choose the correct answers.
3. The lines graphed are coinciding/parallel/intersecting/intersecting and perpendicular.
4. The slopes, m, in each pair of linear equations are equal/not equal.
5. The y-coordinates of the y-intercepts, b, in each pair of linear equations are
equal/not equal.
Write a rule for determining that the graphs of two linear equations in two variables
are coinciding.
Parallel Lines
Chapter 5
Discovery 7
1. Graph the given pairs of linear equations.
a.  2 x  y  4 b. x  2 y  4
c. y  3 x  5
y  2x  5
2 x  4 y  12 3 x  y  6
2. Determine the slope and y-coordinate of the y-intercept for each graph.
a.  2 x  y  4
y  2x  5
b. x  2 y  4
2 x  4 y  12
c. y  3 x  5
3x  y  6
Choose the correct answers.
3. The lines graphed are coinciding/parallel/intersecting/intersecting and perpendicular.
4. The slopes, m, in each pair of linear equations in two variables are equal/not equal.
5. The y-coordinates of the y-intercepts, b, in each pair of linear equations in two
variables are equal/not equal.
Write a rule for determining that the graphs of two linear equations in two variables
are parallel.
Intersecting Lines
Chapter 5
Discovery 8
1. Graph the given pairs of linear equations.
a.  2 x  y  2
y  3x  1
b. x  2 y  4
4 x  4 y  12
c.  3 x  y  6
 3 x  y  6
2. Determine the slope and y-coordinate of the y-intercept for each graph.
a.  2 x  y  2
y  3x  1
b. x  2 y  4
4 x  4 y  12
c.  3 x  y  6
 3 x  y  6
Choose the correct answers.
3. The lines graphed are coinciding/parallel/intersecting/intersecting
and perpendicular.
4. The slopes, m, in each pair of linear equations in two variables are
equal/not equal.
Write a rule for determining that the graphs of two linear equations in
two variables are intersecting.
Perpendicular Lines
1. Graph the given pairs of linear equations.
a.  2 x  3 y  6 b. x  2 y  4
3
y   x2
 8 x  4 y  16
2
Chapter 5
Discovery 9
c.  3 x  y  3
 x  3 y  15
2. Determine the slope and y-coordinate of the y-intercept for each graph.
a.  2 x  3 y  6 b. x  2 y  4
c.  3 x  y  3
3
y   x2
 8 x  4 y  16
 x  3 y  15
2
Choose the correct answers.
3. The lines graphed are coinciding/parallel/intersecting/intersecting and perpendicular.
4. The slopes, m, in each pair of linear equations in two variables are equal/not equal.
5. The two slopes, m, in each pair of linear equations in two variables are reciprocals
and have the same/opposite sign.
Write a rule for determining that the graphs of two linear equations in two variables are
intersecting and perpendicular.