Important Vocabulary Terms The slope of a line

Important Vocabulary Terms The slope of a line is the ratio of the vertical rise to the horizontal run between any two points on the line. You can describe steepness by using slope of a line.

The Slope Ratio vertical rise slope = horizontal run vertical rise = 10 horizontal run = 5 so slope = 10 = 2 5 1 Remember to always simplify the ratio.

Let’s Try It Out! Let’s try and find the slope of a hill that has a vertical rise of 40 ft and a horizontal run of 200 ft. Let m represent the slope. vertical rise = 40 ft horizontal run = 200 ft Don’t touch that button unless you have tried it on your own first! Click the green solution button to check your own work S

Apply the formula- vertical rise to horizontal run Vertical rise = 40 ft Horizontal run = 200 ft 40 ft. ¸ 200 ft. = 1 5 40 Find the GCF The slope of the hill is 1 5 back forward

USING A COORDINATE PLANE TO FIND SLOPE The coordinates are (2, 2) and (6, 5) Use the formula: y . 7 . 5 3 -1 1 3 5 rise run 7 5 -2 3 = 6 -2 = 4

The Slope Of A Line . (x 2, y 2) (x 1, y 1) . y 2 - y 1 x 2 - x 1 The slope m of a line that passes through the points (x 1, y 1) and (x 2, y 2) is rise change in y y 2 - y 1 m = run = change in x = x 2 - x 1

1. Positive Slope 2. Negative Slope 3. Zero Slope 4. Undefined Slope *Continue to click mouse for information* A line that rises from left to right A line falls from left to right A line is horizontal The line is vertical

It’s your turn: Use a piece of graph paper to help you illustrate the slope (x 1, y 1) = (3, 5) and (x 2 , y 2 ) = (1, 4) (x 1, y 1) = (0, 9) and (x 2 , y 2 ) = (4, 7) (x 1, y 1) = (1, 2) and (x 2 , y 2 ) = (5, 2)

(x 1, y 1) = (1, 0) and (x 2 , y 2 ) = (3, 4) y 7 5 3 -1 1 -1 . 1 m= . 3 y 2 - y 1 x 2 - x 1 4 -0 3 -1 m= 4 2 m= 5 7 The slope of the line is 2

(x 1, y 1) = (0, 9) and (x 2 , y 2 ) = (4, 7) . . y m= 7 5 -1 x 2 - x 1 7 -9 4 -0 -1 -2 m= or 4 2 m= 3 1 -1 y 2 - y 1 1 3 5 7 The slope of the line is -1 which makes it a negative slope. 2

(x 1, y 1) = (1, 2) and (x 2 , y 2 ) = (5, 2) y m= 7 5 3 -1 1 -1 . . 1 3 5 y 2 - y 1 x 2 - x 1 2 -2 5 -1 m = 0 or 0 4 m= 7 The slope of the line is zero which makes it a zero slope.

Let’s Review • Slope is the steepness • There are 4 types of of a line slope – positive slope • It is described by a – negative slope ratio of rise to run – zero slope • A coordinate plane can – undefined slope be used to find the slope of a line