Linear Functions Worksheet Page 3
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3858
Chapter 1 LINEAR FUNCTIONS
¡
¢
¡
¢
3
2
5
¡2;
;
:
27. The vertical line through (¡6; 5) goes through the
22. The line goes through
and
4
3
2
point (¡6; 0); so the equation is x = ¡6:
5
3
10
3
¡
¡
2
4
4
4
m =
=
28. The line is horizontal, through (8; 7):
2
2
6
¡ (¡2)
+
3
3
3
The line has an equation of the form y = k where
7
21
k is the y-coordinate of the point. In this case,
4
=
=
8
32
k = 7; so the equation is y = 7:
3
3
21
29. Write an equation of the line through (¡4; 6), par-
y ¡
=
[x ¡ (¡2)]
4
32
allel to 3x + 2y = 13:
3
21
42
Rewrite the equation of the given line in slope-
y ¡
=
x +
4
32
32
intercept form.
21
42
3
y =
x +
+
3x + 2y = 13
32
32
4
2y = ¡3x + 13
21
21
12
y =
x +
+
32
16
16
3
13
y = ¡
x +
21
33
2
2
y =
x +
32
16
3
The slope is ¡
:
2
3
Use m = ¡
and the point (¡4; 6) in the point-
23. The line goes through (¡8; 4) and (¡8; 6):
2
slope form.
4 ¡ 6
¡2
3
m =
=
y ¡ 6 = ¡
[x ¡ (¡4)]
¡8 ¡ (¡8)
0
2
3
which is unde…ned.
y = ¡
(x + 4) + 6
2
This is a vertical line; the value of x is always ¡8:
3
The equation of this line is x = ¡8:
y = ¡
x ¡ 6 + 6
2
24. The line goes through (¡1; 3) and (0; 3):
3
y = ¡
x
2
3 ¡ 3
0
m =
=
= 0
30. Write the equation of the line through (2; ¡5);
¡1 ¡ 0
¡1
parallel to y ¡ 4 = 2x: Rewrite the equation in
This is a horizontal line; the value of y is always
slope-intercept form.
3. The equation of this line is y = 3:
y ¡ 4 = 2x
25. The line has x-intercept ¡6 and y-intercept ¡3.
y = 2x + 4
Two points on the line are (¡6; 0) and (0; ¡3).
The slope of this line is 2.
Find the slope; then use slope-intercept form.
Use m = 2 and the point (2; ¡5) in the point-slope
¡3 ¡ 0
¡3
1
m =
=
= ¡
form.
0 ¡ (¡6)
6
2
y ¡ (¡5) = 2(x ¡ 2)
b = ¡3
y + 5 = 2x ¡ 4
y = 2x ¡ 9
1
y = ¡
x ¡ 3
2
31. Write an equation of the line through (3; ¡4); per-
pendicular to x + y = 4:
26. The line has x-intercept ¡2 and y-intercept 4.
Rewrite the equation of the given line as
Two points on the line are (¡2; 0) and (0; 4): Find
y = ¡x + 4:
the slope; then use slope-intercept form.
The slope of this line is ¡1: To …nd the slope of a
4 ¡ 0
4
m =
=
= 2
0 ¡ (¡2)
2
perpendicular line, solve
y = mx + b
¡1m = ¡1:
y = 2x + 4
m = 1
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