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Math 9
Unit 4: Linear Relations
Section 4.3: Another form of the equation of a linear relation
Terminology
Parallel Lines: Lines that run in the same direction and never touch.
Perpendicular Lines: Lines that cross each other at a 90° angle.
Vertical Line: a line that extends up and down. Runs parallel to the y-axis and perpendicular
to the x-axis.
Horizontal Line: a line that extends left and right. Runs parallel to the x-axis and
perpendicular to the y-axis.
Oblique Line: a line that is drawn at an angle. Runs neither parallel nor perpendicular to
either axis on a graph.
Graphing and Describing Horizontal and Vertical Lines (Text Page 178 #4, 5, 6, 7, 8, 12)
The graph of the equation x = a , where a
is a constant, is a vertical line that passes
through the a on the x-axis. Every point on
the graph has an x-coordinate of a.
The graph of the equation y = a , where a
is a constant, is a horizontal line that passes
through the a on the y-axis. Every point on
the graph has an y-coordinate of a.
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Math 9
Unit 4: Linear Relations
1. For each equation
i.
Graph the equation
ii.
Describe the graph
a.
x = -4
b.
y+2=0
c.
2x = 5
2. Does each of the following describe a vertical line, horizontal line, or an oblique line?
a. x = -5
b. y – 2 = 0
c. 3x + y – 12 = 0
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Math 9
Unit 4: Linear Relations
3. Write an equation and describe the line in the graph provided.
a.
b.
y
y
1
- 10
10
-5
5
x
10
5
-1
-2
-1
1
2
3
x
-3
-5
-4
-5
- 10
4. Which equation best describes the graph given?
a.
b.
x–3=0
3x + 6 = 0
c.
d.
3y – 6 = 0
3x – 6 = 0
y
10
5
-4
-3
-2
-1
1
2
x
-5
- 10
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Math 9
Unit 4: Linear Relations
Graphing an equation in the form ax + by = c (Text Page 178 #10, 11, 14, 15, 17, 21)
When given an equation that does not have y by itself, we can rearrange the equation first
so that it is in slope-intercept form.
1. Rearrange each of the following equations to slope-intercept form.
a.
b.
c. x + y = 5
4x + 3y = 12
-2x – 2y = 6
d.
1x–1y=1
4
2
e.
1x+1y=6
2
3
f.
-2.5x + 0.5y = 7
2. For the equation 3x – 2y = 6
a. Make a table of values for -4, 0, 4.
b. Graph the equation.
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Math 9
Unit 4: Linear Relations
3. The difference of two numbers is 8. Let x represent the greater number and y represent
the lesser number.
a. Complete a table for 8 different values of x.
b. Graph the data. Should you join the points?
c. Write an equation that relates x and y.
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