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Do Now

Solve problems in notebook: find slope, graph equations, do unit retake, and test corrections. Objective: graph linear equations, plot points, connect dots.

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Do Now

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  1. Do Now 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.

  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 6.0Students graph a linear equationand 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. Rules for Graphing in Slope-intercept formy = mx + b • 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.

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

  6. Step 2The slope is 1/2 . 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.

  7. Step 3The slope is Example 2: Graph 5x + 4y = 8. Step 1Write the equation in slope-intercept form 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.

  8. Step 2 Slope = Count 2 units down and 5 units right from (0, 4) and plot another point. 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). y • Rise = –2 • • • Run = 5 Step 3 Draw the line through the two points.

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

  10. slope: m = 3 = y-intercept: b = –1 Example 5: Graph y = 3x – 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. slope: m = y-intercept: b = 3 Example 6: Graph 2y + 3x = 6 Step 1 Write the equation in slope-intercept form. Step 2 Graph the line. • • 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. Step 2 Slope = Count 2 units up and 1 unit right from (0, –3) and plot another point. 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). Run = 1 • Rise = 2 • Step 3 Draw the line through the two points.

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

  14. y = x + 0 is in slope-intercept form YOU TRY! #3 Graph the line described by the equation. • • slope: m = 2/3 & y-intercept: b = 0 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.

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

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

  17. YOU TRY! #6 Graph y = 2x – 4

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

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

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