1. Objective: To graph lines given their equations.
Chapter 3 Lesson 5
Objective: To graph lines given their equations.

2. y = mx + b y-intercept slope
Slope-Intercept Form: a linear equation y=mx+b, where m is the slope of the line and b is the y-intercept.
y = mx + b
y-intercept
slope
**Remember: Postulate 1-1 states that two points determine a line.**

3. Example 1: Graphing Lines in Slope-Intercept Form2 4 6 8 -2 -4 -6
Move right units
Graph the line
Move up 3 units
Start at (0,2)
Slope
y-intercept

4. Example 2: Graphing Lines in Slope-Intercept Form4 6 8 -2 -4 -6
Graph the line
Start at (0,-2)
Slope
y-intercept
Move right 2 units
Move down 1 unit

5. Example 3: Graphing Lines in Slope-Intercept Form2 4 6 8 -2 -4 -6
Start at (0,9)
Move down 2 units
Use the slope and y-intercept to graph the line y=-2x or
Move right 1 unit
Slope
y-intercept

6. Example 4: Graphing Lines Using Intercepts
standard form of a linear equation: Ax+By=C, where A,B, and C are real numbers and A and B are not both zero.
Example 4: Graphing Lines Using Intercepts
Graph 6x + 3y = 12
Step 2: To find the x-intercept substitute 0 for y; solve for x.
Step 1: To find the y-intercept substitute 0 for x; solve for y.
6x + 3y = 12
6(0) + 3y = 12
3y = 12
y = 4
(0,4)
6x + 3y = 12
6x + 3(0) = 12
6x = 12
x = 2
(2,0)

7. Example 4 (cont.): Graphing Lines Using Intercepts2 4 6 8 -2 -4 -6

8. Example 5: Graphing Lines Using Intercepts
Graph -2x + 4y = -8
Step 2: To find the x-intercept substitute 0 for y; solve for x.
Step 1: To find the y-intercept substitute 0 for x; solve for y.
-2x + 4y = -8
-2(0) + 4y = -8
4y = -8
y = -2
(0,-2)
-2x + 4y = -8
-2x + 4(0) = -8
-2x = -8
x = 4
(4,0)

9. Example 5 (cont.) : Graphing Lines Using Intercepts2 4 6 8 -2 -4 -6

10. Example 6: Transforming to Slope-Intercept Form
Graph 4x - 2y = 9
Step 1: Transform the equation to slope-intercept form.
y=mx+b
Slope
y-intercept

11. Example 6 (cont.) : Transforming to Slope-Intercept Form2 4 6 -2 -4 -6
Step 2: Use the y-intercept and the slope to plot two points and draw the line containing them.
Slope
y-intercept

12. Example 7: Transforming to Slope-Intercept Form
Transform the equation -6x + 3y = 12 to slope-intercept form, and then graph the resulting equation.
Step 1: Transform the equation to slope-intercept form.
y=mx+b
Slope
y-intercept

13. Example 7 (cont.) : Transforming to Slope-Intercept Form2 4 6 8 -2 -4
Step 2: Use the y-intercept and the slope to plot two points and draw the line containing them.
Slope
y-intercept

14. Homework
Page 155 – 156
#1-16; ; 45-46; 48-51