1. Algebra 1
Section 6.5

2. Linear Equations Standard form: Ax + By = C
Slope-intercept form: y = mx + b
Point-slope form:
y – y1 = m(x – x1)

3. Point-Slope Form of a Line
The point-slope form provides an alternative method of determining the equation of a line from the slope (m) and any given point (x1, y1) on the line.

4. Example 1 Equation of the line passing through (-5, 2) and (3, -4):
First, find the slope:
m =
y2 – y1
x2 – x1
-4 - 2
3 -(-5) = -6 8 = 3 4
= -

5. Example 1 y – y1 = m(x – x1) y -(-4) = -¾(x – 3) y + 4 = - x + 3 4 97

6. Example 1
y = x – 3 4 7
To standard form:
4y = -3x – 7
3x + 4y = -7

7. Definitions
Parallel lines are lines in the same plane that have no points in common.
Perpendicular lines meet at right angles (90°).

8. Parallel Lines
The graphs of linear equations are parallel if they have the same slope but different y- intercepts.

9. Example 2 3x – y = 6 y = 3x – 6 m1 = 3 y-int: (0, -6) -9x + 3y = 12
The lines are parallel.

10. Example 3 Find the slope of 4x + 3y = 17. 4 m = - 3
The parallel line has the same slope, and goes through the point (-5, 9).

11. Example 3 y – y1 = m(x – x1) y – 9 = - [x -(-5)] 4 3 y – 9 = - x – 4 320
y = x + 4 3 7

12. Slopes Parallel lines have the same slope.
Perpendicular lines have slopes that are negative reciprocals of each other.

13. Number Negative Reciprocal
Example 4
Number Negative Reciprocal 8 5 5 8 - 1 9 - 9

14. Number Negative Reciprocal
Example 4
Number Negative Reciprocal 13 7 - 7 13 1 a - a

15. Example 5 The slope of y = -4x + 9 is -4.
Find the slope of a line perpendicular to it: 1 4
m =
The perpendicular line has a slope of ¼, and goes through the point (2, 7).

16. The lines are neither parallel nor perpendicular.
Example 6
2x + 5y = 9
4x + y = 1
y = -4x + 1
m2 = -4
y = x + 2 5 9 2 5
m1 = -
The lines are neither parallel nor perpendicular.

17. Homework: pp