1. Objectives
Graph lines and write their equations in slope-intercept and point-slope form.
Classify lines as parallel, intersecting, or coinciding.

2. A system of two linear equations in two variables represents two lines
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.

4. 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.

5. 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
Both lines have a slope of , and the y-intercepts are different. So the lines are parallel.

6. 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.

7. 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.

8. 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?

9. Solve 3
Plan A: y = 0.35x + 100
Plan B: y = 0.50x + 85
Subtract the second equation from the first.
0 = –0.15x + 15
x = 100
Solve for x.
Substitute 100 for x in the first equation.
y = 0.50(100) + 85 = 135

10. Solve Continued 3
The lines cross at (100, 135).
Both plans cost $135 for 100 miles.

11. Look Back 4
Check your answer for each plan in the original problem.
For 100 miles, Plan A costs
$ $0.35(100) = $100 + $35 = $
Plan B costs $ $0.50(100) = $85 + $50 = $135, so the plans cost the same.

12. Lesson Quiz: Part II
Determine whether the lines are parallel, intersect, or coincide. 1 2
3. y – 3 = – x,
y – 5 = 2(x + 3)
intersect
4. 2y = 4x + 12, 4x – 2y = 8
parallel