Slope of a Line Chapter 7.3. 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.

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Presentation transcript:

Slope of a Line Chapter 7.3

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.

Positive Slope Lines going up to the right.

Negative Slope Lines going down to the right.

Zero Slope Horizontal lines.

No Slope or Undefined Slope Vertical lines.

m = y2y2 x2x2 (x 1, y 1 ) (x 2, y 2 ) m = Find the slope of a line that passes through (, ) and (, ) m = 1 5 – y1y1 – x1x – – 1 6 Substitute Subtract Simplify

m = y2y2 x2x2 (x 1, y 1 ) (x 2, y 2 ) m = Find the slope of a line that passes through (, ) and (, ) m = 3 – y1y1 – x1x – – 0 2 Substitute Subtract Simplify

m = y2y2 x2x2 (x 1, y 1 ) (x 2, y 2 ) m = a. Find the slope of a line that passes through (, ) and (, ) no slope – y1y1 – x1x – – 6 ( - 5) Substitute Subtract Simplify or undefined slope

m = y2y2 x2x2 (x 1, y 1 ) (x 2, y 2 ) m = b. Find the slope of a line that passes through (, ) and (, ) m = – y1y1 – x1x – – ( - 11) ( - 7) Substitute Subtract Simplify 0

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).

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 – y = 2 x m = 2 y-intercept = 5 2 (0, )

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 +

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

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.

6. Graph the line with a slope = and a y-intercept = (0, ) 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.

7. Graph the equation: y = x 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.

Slope of a Line Chapter 7.3