Slope - Intercept And Point-Slope Forms Of The Line Worksheet With Answers - Hfcc Math Lab Page 4
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82.
Find the equation of the line passing through the point (3, 5) and (3, -4)
First, we need to find the slope m:
y
y
4 5
9
2
1
m
undefined where ( , ) (3,5) & ( ,
x y
x y
) (3, 4)
1
1
2
2
x
x
3 3
0
2
1
m is undefined, the line is vertical. Therefore, the equation of the line is x = 3.
IV.
EQUATION OF A VERTICAL LINE: The slope of a vertical line is undefined.
The equation of a vertical line passing through the point
( , ) is
x y
x
x
1
1
1
Examples:
1. Find the equation of the vertical line passing through the point (-7, 6).
The equation of the line is x = -7.
2. Find the equation of the line with undefined slop and x-intercept 8.
( , )
x y
= (8, 0). Therefore, the equation of the line is x = 8.
1
1
3. Find the equation of the line passing through the points (4, 3) and (4, -2).
First, we need to find the slope m:
y
y
2 3
5
2
1
m
undefined where ( , ) (4,3) & ( ,
x y
x y
) (4, 2)
1
1
2
2
x
x
4 4
0
2
1
Therefore, the equation of the vertical line is x = 4.
V.
Given the equation of a non-vertical line, you can find the slope and y-intercept by
rewriting the equation in slope-intercept form (y = mx+b) and then reading the values
of m and b.
Examples:
1. Find the slope and y-intercept of the line 2x + y = 5.
First, we need to solve for y:
2
x y
5
2
x
2
x y
2
x
5 [subtract 2x from both sides]
y
2 5
x
y
mx b
, m = -2 and b = 5
Therefore, the slope is -2 and the y-intercept (0, 5).
2. Find the slope and y-intercept of the line 3x +6y = 2.
First, we need to solve for y:
Revised 11/09
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