Graph lines and write their equations in slope-intercept and point-slope form.

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Objectives
Graph lines and write their equations in
slope-intercept and point-slope form. Classify
lines as parallel, intersecting, or coinciding.
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A system of two linear equations in two variables
represents two lines. The lines can be parallel,
intersecting, or coinciding. Lines that coincide
are the same line, but the equations may be
written in different forms.
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Example 3A Classifying Pairs of Lines
Determine whether the lines are parallel,
intersect, or coincide.
y 3x 7, y 3x 4
The lines have different slopes, so they
intersect.
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Example 3B Classifying Pairs of Lines
Determine whether the lines are parallel,
intersect, or coincide.
Solve the second equation for y to find the
slope-intercept form.
6y 2x 12
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Example 3C Classifying Pairs of Lines
Determine whether the lines are parallel,
intersect, or coincide.
2y 4x 16, y 10 2(x - 1)
Solve both equations for y to find the
slope-intercept form.
2y 4x 16
y 10 2(x 1)
2y 4x 16
y 10 2x - 2
y 2x 8
y 2x 8
Both lines have a slope of 2 and a y-intercept of
8, so they coincide.
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Check It Out! Example 3
Determine whether the lines 3x 5y 2 and 3x
6 -5y are parallel, intersect, or coincide.
Solve both equations for y to find the
slope-intercept form.
3x 5y 2
3x 6 5y
5y 3x 2
Both lines have the same slopes but different
y-intercepts, so the lines are parallel.
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Example 4 Problem-Solving Application
Erica is trying to decide between two car rental
plans. For how many miles will the plans cost the
same?
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Plan A y 0.35x 100
Plan B y 0.50x 85
Subtract the second equation from the first.
x 100
Solve for x.
Substitute 100 for x in the first equation.
y 0.50(100) 85 135
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The lines cross at (100, 135).
Both plans cost 135 for 100 miles.
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Check your answer for each plan in the original
problem. For 100 miles, Plan A costs 100.00
0.35(100) 100 35 135.00. Plan B
costs 85.00 0.50(100) 85 50 135, so
the plans cost the same.
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Lesson Quiz Part II
Determine whether the lines are parallel,
intersect, or coincide.
3. y 3 x,
y 5 2(x 3)
intersect
4. 2y 4x 12, 4x 2y 8
parallel