Do Now 2/8/12 In your notebook, answer the following question. There are two skateboard ramps at a skate park. One ramp is 12 ft long and 6 ft tall.

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Do Now 2/8/12 In your notebook, answer the following question. There are two skateboard ramps at a skate park. One ramp is 12 ft long and 6 ft tall. The other is 10 ft long and 8 ft tall. Which ramp do you think is steeper? How can you tell?

Objective SWBAT find the slope of a line and interpret slope as a rate of change

Section 8.4 “The Slope of a Line” the ratio of the vertical change (the rise) to the horizontal change (the run) between any two points on a line. Slope = rise = change in y run change in x

Slope Symbols The slope m of a line passing through two points and is the ratio of the rise change to the run. y run rise “positive slope” x

Slope Symbols The slope m of a line passing through two points and is the ratio of the rise change to the run. y rise run x “negative slope”

Find a positive slope Find the slope of the line shown. Let (x1, y1) = (–4, 2) = (x2, y2) = (2, 6). m = y2 – y1 x2 – x1 Write formula for slope. 6 – 2 2 – (– 4) = Substitute. = 4 6 2 3 Simplify.

Find the slope of the line that passes through the points. (5, 2) and (4, –1) Let (x1, y1) = (5, 2) = (x2, y2) = (4, – 1). m = y2 – y1 x2 – x1 Write formula for slope. (– 1) – 2 4 – 5 = Substitute. = – 3 –1 = 3 Simplify.

Find a negative slope XAMPLE 2 Find the slope of the line shown. Let (x1, y1) = (3, 5) and (x2, y2) = (6, –1). m = y2 – y1 x2 – x1 Write formula for slope. –1 – 5 6 – 3 = Substitute. – 6 3 = –2 Simplify.

Find the slope of the line that passes through the points (0, 6) and (5, –4) Let (x1, y1) = (0, 6) and (x2, y2) = (5, – 4). m = y2 – y1 x2 – x1 Write formula for slope. – 4 – 6 5 – 0 = Substitute. 10 5 = – = – 2 Simplify.

Find the slope of a horizontal and vertical line Find the slope of the line shown. Let (x1, y1) = (– 2, 4) and (x2, y2) = (4, 4). m = y2 – y1 x2 – x1 Write formula for slope. 4 – 4 4 – (– 2) = Substitute. 6 = Simplify. EXAMPLE 4 Find the slope of the line shown. Let (x1, y1) = (3, 5) and (x2, y2) = (3, 1). m = y2 – y1 x2 – x1 Write formula for slope. 1 – 5 3 – 3 = Substitute. – 4 = Division by zero is undefined.

Identifying Slopes y2 – y1 m = x2 – x1 Positive slope Undefined Slope of 0 Negative slope

Section 8.4 “Investigating Slope” With a partner, complete the concept activity “Investigating Slope” on page 403 in your textbook.