1. Complete the following problems in your lecture notebook, QUIETLY. 1) Find the slope of the line given (2, 3) and (-3, -2). 2) Write the equation y – 5 = 6(x – 8) in slope-intercept form. 3) Write the equation y + 7 = -8(x + 5) in slope-intercept form. Announcements: Unit 1 Retake is tomorrow after school. Unit 1 Test Corrections are due 9/19/12. Do Now

2. Students will be able to demonstrate their understanding of graphing linear equations by correctly graphing at least 3 of the 4 linear equations on their exit slip. Objective Ex. x – y = 6  y = x – 6

3. Standard 6.0 Students graph a linear equation and compute the x- and y- intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4).

4. Step 1: Plot your y-intercept on your graph. Step 2: Rewrite your slope as a fraction. Step 3: The numerator is the vertical change (RISE) & the denominator is the horizontal change (RUN). Step 4: Graph at least 2 points and connect the dots. Rules for Graphing in Slope-intercept form y = mx + b

5. Step 1: Rewrite your equation in slope- intercept form. Follow the steps for Graphing in slope- intercept form. Rules for Graphing in Standard form. Ax + By = C

6. Example 1: Graph y = ½x – 7. Step 1The y-intercept is –7. So graph (0, –7). From (0, –7), move up 1 unit and right 2 units. Draw a dot. Step 3Draw a line through the points. Step 2The slope is 1/2.

7. Example 2: Graph 5x + 4y = 8. Step 2The y-intercept is 2, so graph (0, 2). From (0, 2), move down 5 units and right 4 units. Draw a dot. Draw a line connecting the points. Step 3The slope is Step 1Write the equation in slope-intercept form

8. Example 3: Graph the line given the slope & y-intercept. y intercept = 4 Step 1 The y-intercept is 4, so the line contains (0, 4). Plot (0, 4). Step 3 Draw the line through the two points. Run = 5 Rise = –2 Step 2 Slope = Count 2 units down and 5 units right from (0, 4) and plot another point. y

9. slope = 4; y-intercept = Step 1 The y-intercept is, so the line contains (0, ). Plot (0, ). Step 3 Draw the line through the two points. Rise = 4 Run = 1 Example 4: Graph the line given the slope and y- intercept. Step 2 Slope = Count 4 units up and 1 unit right from (0, ) and plot another point.

10. Example 5: Graph y = 3x – 1 slope: m = 3 = y-intercept: b = –1 Step 1 Plot (0, –1). Step 2 Count 3 units up and 1 unit right and plot another point. Step 3 Draw the line connecting the two points.

11. Example 6: Graph 2y + 3x = 6 Step 1 Write the equation in slope-intercept form. Step 2 Graph the line. slope: m = y-intercept: b = 3 Plot (0, 3). Step 3 Count 3 units down and 2 units right and plot another point. Draw the line connecting the two points.

12. YOU TRY! #1 Graph the line given the slope and y-intercept. slope = 2, y-intercept = –3 Step 1 The y-intercept is –3, so the line contains (0, –3). Plot (0, –3). Step 3 Draw the line through the two points. Rise = 2 Run = 1 Step 2 Slope = Count 2 units up and 1 unit right from (0, –3) and plot another point.

13. Graph each line given the slope and y-intercept. slope =, y-intercept = 1 YOU TRY! #2 Step 1 The y-intercept is 1, so the line contains (0, 1). Plot (0, 1). Step 3 Draw the line through the two points. Rise = –2 Run = 3 Step 2 Slope = Count 2 units down and 3 units right from (0, 1) and plot another point.

14. YOU TRY! #3 Graph the line described by the equation. Step 1 Plot (0, 0). Step 2 Count 2 units up and 3 units right and plot another point. Step 3 Draw the line connecting the two points. y = x + 0 is in slope-intercept form slope: m = 2/3 & y-intercept: b = 0

15. YOU TRY! #4 6x + 2y = 10 Step 1 Write the equation in slope intercept form. Write the equation in slope-intercept form. Then graph the line described by the equation. Step 2 Graph the line. y-intercept: b = 0 Plot (0, 5). slope: m = Count 3 units down and 1 unit right and plot another point. Draw the line connecting the two points. y = –3x + 5

16. YOU TRY! #5 y = –4 Step 1 Plot (0, –4). y = –4 is in the form y = mx + b. y-intercept: b = –4 slope: m = 0 = = 0 Since the slope is 0, the line will be a horizontal at y = –4. Graph the line described by the equation.

17. Graph y = 2x – 4 YOU TRY! #6

18. Graph 3x + 2y = 6. YOU TRY! #7

19. Write the equation in slope-intercept form and then graph the line. 6x + 2y = 10 y = –3x + 5 Reminder by the end of this lesson you will be expected to do this.