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# Section 4.7

Section 4.7. Slope-Intercept Form. Coordinated Plane. Graphing Lines. A line is the graph of a linear equation in the form . This is called the Slope-Intercept form of the line because: m is the slope and b is the y-intercept. Identifying the slope and y-intercept. y = 2 x + 1

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## Section 4.7

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1. Section 4.7 Slope-Intercept Form

2. Coordinated Plane

3. Graphing Lines • A line is the graph of a linear equation in the form . • This is called the Slope-Intercept form of the line because: • m is the slope and • b is the y-intercept.

4. Identifying the slope and y-intercept y = 2x + 1 m = 2 b = 1 y = -2x m = -2 b = 0 y = 5x - 3 m = 5 b = -3

5. Your Turn m = 12 b = -15 y = 12x - 15 y = -4x m = -4 b = 0 b = 4

6. Putting into Slope-intercept • You can only find the slope and y-intercept if the equation is in slope-intercept form. • If it is in any other form you need to solve for y.

7. Solving for y 2x + 3y = 6 -2x -2x 3y = -2x + 6 3 3

8. Your Turn 5x + 3y = 15 -5x -5x 3y = -5x + 15 3 3

9. Writing the Equation of a Line • To write the equation of a line, you must know the slope, m, and the y-intercept, b. • If it is in the form of y =mx + b, you have both the slope and the y-intercept. • If it is not in slope-intercept form, you need solve for y in order to find m and b.

10. Graphing Lines • Plot the y-intercept on the y-axis. • Obtain a second point by using the slope, starting from the y-intercept. • If the slope is positive go up if it is negative go down, going the same number of spaces as the top number. • Then go to the right or positive direction the same number of spaces as the bottom number. • Use a straightedge to connect the dots. • Remember – A line continues infinitely in both directions, so put arrows on the end of your lines.

11. Example 1 • Graph y = 2x+1. m = 2 = 2/1 b = 1

12. Example 2 b = -2

13. Your Turn • Graph y = 3x + 2 • m = 3 = 3/1 • b = 2

14. Example 3 4x + 2y = 6 -4x -4x 2y = -4x + 6 2 2 y = -2x + 3 m = - 2 = -2/1 b = 3

15. Your Turn 6x - 3y = 9 -6x -6x -3y = -6x + 9 -3 -3 y = 2x - 3 m = 2 = 2/1 b = - 3

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