Algebraic Manipulation Worksheets With Answers - Craven Community College Page 20
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29Example:
Find the slope of the line though (-2, -3) and (2, 5)
m=5 – (-3) = 8
=
2
2 – (-2)
4
1
Thus the slope is 2.
Parallel lines are two distinct lines which do not intersect and have the same slope.
Perpendicular lines are two distinct lines which intersect at right angles. In perpendicular lines, the
product of the slopes of the line is -I. The slopes of perpendicular lines are opposite reciprocals.
Writing Equations of Lines
The slope intercept form of the line is used in writing the equation of a line. First the slope is determined
from the given information. The y- intercept is then determined by using this slope and any given point.
From this information the equation of the line is written.
Example:
Write the equation of the line through (5, 1) and (-3, -7)
m = -7 – 1 = -8 = 1
Determine the slope
-3 – 5 -8
Y = mX + b
Slope intercept form of line
1 = 1(5) + b
Substitute m = I and point (5, 1)
-4 = b
Solve for y-intercept
Y=X – 4
Equation of a line
Example:
Write the equation of a line parallel to Y = 6X – 1 and through the point (-1, -2)
M = 6
Read slope from line
Y = mX + b
Slope intercept form of the line
-2 = 6(-1) + b
Substitute m = 6 and point (-1, -2)
4 = b
Solve for b
Y = 6X + 4
Equation of the line
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