Linear Functions Worksheet
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38Chapter 1
LINEAR FUNCTIONS
8. 4x + 7y = 1
1.1
Slopes and Equations of Lines
Rewrite the equation in slope-intercept form.
1. Find the slope of the line through (4; 5) and (¡1; 2):
5 ¡ 2
7y = 1 ¡ 4x
m =
4 ¡ (¡1)
1
1
1
(7y) =
(1) ¡
(4x)
3
7
7
7
=
5
1
4
y =
¡
x
7
7
2. Find the slope of the line through (5; ¡4) and
4
1
(1; 3):
y = ¡
x +
7
7
3 ¡ (¡4)
m =
1 ¡ 5
4
The slope is ¡
:
3 + 4
7
7
=
= ¡
¡4
4
9. x = 5
3. Find the slope of the line through (8; 4) and (8; ¡7):
4 ¡ (¡7)
This is a vertical line. The slope is unde…ned.
m =
8 ¡ 8
11
=
10. The x-axis is the horizontal line y = 0: Horizontal
0
lines have a slope of 0.
The slope is unde…ned; the line is vertical.
4. Find the slope of the line through (1; 5) and (¡2; 5):
11. y = 8
5 ¡ 5
0
m =
=
= 0
This is a horizontal line, which has a slope of 0.
¡2 ¡ 1
¡3
5. y = x
12. y = ¡6
Using the slope-intercept form, y = mx + b, we
By rewriting this equation in the slope-intercept
see that the slope is 1.
form, y = mx + b; we get y = 0x ¡ 6; with the
slope, m; being 0.
6. y = 3x ¡ 2
This equation is in slope-intercept form,
13. Find the slope of a line parallel to 6x ¡ 3y = 12:
y = mx + b. Thus, the coe¢cient of the x-term,
3, is the slope.
Rewrite the equation in slope-intercept form.
7. 5x ¡ 9y = 11
¡3y = ¡6x + 12
Rewrite the equation in slope-intercept form.
y = 2x ¡ 4
9y = 5x ¡ 11
5
11
The slope is 2, so a parallel line will also have slope
y =
x ¡
9
9
2.
5
:
The slope is
9
56
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