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Use the slope and y -intercept to graph the line y = –2 x + 9.

Lines in the Coordinate Plane. LESSON 3-6. Additional Examples. Use the slope and y -intercept to graph the line y = –2 x + 9. When an equation is written in the form y = m x + b , m is the slope and b is the y -intercept .

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Use the slope and y -intercept to graph the line y = –2 x + 9.

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  1. Lines in the Coordinate Plane LESSON 3-6 Additional Examples Use the slope and y-intercept to graph the line y = –2x + 9. When an equation is written in the form y = mx + b, m is the slope and b is the y-intercept. In the equation y = –2x + 9, the slope is –2 and the y-intercept is 9. Quick Check

  2. Lines in the Coordinate Plane LESSON 3-6 Additional Examples Use the x-intercept and y-intercept to graph 5x – 6y = 30. To find the x-intercept, substitute 0 for y and solve for x. To find the y-intercept, substitute 0 for x and solve for y. 5x – 6y = 30 5x – 6(0) = 30 5x – 0 = 30 5x = 30 x = 6 5x – 6y = 30 5(0) – 6y = 30 0 – 6y = 30 –6y = 30 y = –5 The x-intercept is 6. A point on the line is (6, 0). The y-intercept is –5. A point on the line is (0, –5).

  3. Lines in the Coordinate Plane LESSON 3-6 Additional Examples (continued) Plot (6, 0) and (0, –5). Draw the line containing the two points. Quick Check

  4. Step 2: Use the y-intercept and the slope to plot two points and draw the line containing them. –6x + 3y = 12 3y = 6x + 12 Add 6x to each side. = + Divide each side by 3. y = 2x + 4 3y 3 6x 3 12 3 Lines in the Coordinate Plane LESSON 3-6 Additional Examples Transform the equation –6x + 3y = 12 to slope-intercept form, then graph the resulting equation. Step 1: Transform the equation to slope-intercept form. The y-intercept is 4 and the slope is 2. Quick Check

  5. Lines in the Coordinate Plane LESSON 3-6 Additional Examples Write an equation in point-slope form of the line with slope –8 that contains P(3, –6). y – y1 = m(x – x1) Use point-slope form. y – (–6) = –8(x – 3) Substitute –8 for m and (3, –6) for (x1, y1). y + 6 = –8(x – 3) Simplify. Quick Check

  6. y2 – y1 x2– x1 Use the formula for slope. Substitute (4, –9) for (x1, y1)and (–1, 1) for (x2, y2). Simplify. m = –2 m = 1 – (–9) –1 – 4 m = 10 –5 m = Lines in the Coordinate Plane LESSON 3-6 Additional Examples Write an equation in point-slope form of the line that contains the points G(4, –9) and H(–1, 1). Step 1: Find the slope.

  7. Lines in the Coordinate Plane LESSON 3-6 Additional Examples (continued) Step 2: Select one of the points. Write the equation in point-slope form. y – y1 = m(x – x1) Point-slope form y – (–9) = –2(x – 4) Substitute –2 for mand (4, –9) for (x1, y1). y + 9 = –2(x – 4) Simplify. Quick Check

  8. Lines in the Coordinate Plane LESSON 3-6 Additional Examples Write equations for the horizontal line and the vertical line that contain A(–7, –5). Every point on the horizontal line through A(–7, –5) has the same y-coordinate, –5, as point A. The equation of the line is y = –5. It crosses the y-axis at (0, –5). Every point on the vertical line through A(–7, –5) has the same x-coordinate, –7, as point A. The equation of the line is x = –7. It crosses the x-axis at (–7, 0). Quick Check

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