1. Slope of a Line Chapter 7.3

2. Slope of a Line m = y 2 – y 1 x 2 – x 1 m = rise run m = change in y change in x Given two points (x 1, y 1 ) and (x 2, y 2 ) There are three ways to describe the slope (m) of a line.

3. Positive Slope Lines going up to the right.

4. Negative Slope Lines going down to the right.

5. Zero Slope Horizontal lines.

6. No Slope or Undefined Slope Vertical lines.

7. m = y2y2 x2x2 (x 1, y 1 ) (x 2, y 2 ) - 1 - 4 m = -2 -10 1. Find the slope of a line that passes through (, ) and (, ) m = 1 5 – y1y1 – x1x1 -1 -4-4 1 6 – – 1 6 Substitute Subtract Simplify

8. m = y2y2 x2x2 (x 1, y 1 ) (x 2, y 2 ) 1 - 1 m = 1 -3 2. Find the slope of a line that passes through (, ) and (, ) m = 3 – y1y1 – x1x1 1 -1 0 2 – – 0 2 Substitute Subtract Simplify

9. m = y2y2 x2x2 (x 1, y 1 ) (x 2, y 2 ) 3 - 5 m = -3 0 3a. Find the slope of a line that passes through (, ) and (, ) no slope – y1y1 – x1x1 3 -5-5 6 -5-5 – – 6 ( - 5) Substitute Subtract Simplify or undefined slope

10. m = y2y2 x2x2 (x 1, y 1 ) (x 2, y 2 ) - 11 3 m = 0 10 3b. Find the slope of a line that passes through (, ) and (, ) m = – y1y1 – x1x1 - 11 3 -7-7 – – ( - 11) ( - 7) Substitute Subtract Simplify 0

11. Slope-Intercept Form An equation of a line can be written in slope- intercept form where m is the slope and b is the y-intercept. y = mx + b The y-intercept is a point on the y-axis with the coordinates (0, b).

12. 4. Find the slope and y-intercept of a line given the following equation. 4x – 2y = -5 Write in slope-intercept form, y = mx + b -4x -4x -2y = -4x – 5 -2 -2 -2 y = 2 x + 5 2 m = 2 y-intercept = 5 2 (0, )

13. 5a. Write the equation in slope-intercept form of a line given the following. Write in slope-intercept form, y = mx + b y = -3 7 slope = y-intercept = 2 7 (0, ) -3 7 x 2 7 +

14. 5b. Write the equation in Standard Form: Ax + By = C. A, B, and C are integers, and A is positive. y = -3 7 x 2 7 + 7( ) 7( ) 7( ) 7y = +3x +3x -3x + 2 3x + 7y = 2 1 1

15. Graphing an equation using the Slope-intercept Form 1. May have to rewrite the equation into y = mx + b. 2. Plot the y-intercept (b) on the y-axis. 3. Use the slope to plot 2 more points. 4. Draw a straight line through them.

16. 6. Graph the line with a slope = and a y-intercept = (0, ). 3 4 1. Plot the y-intercept. 2. Use the slope to plot two more points. 3. Draw the line. move up 3, right 4. move down 3, left 4.

17. 7. Graph the equation: y = x -2 3 1. Plot the y-intercept. 2. Use the slope to plot two more points. 3. Draw the line. + 5 move down 2, right 3. move up 2, left 3.

18. Slope of a Line Chapter 7.3