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Do Now 10/29/09 Copy HW in your planner. Text page 239, #4-32 even 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?

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

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Section 4.4 “Find Slope and Rate of Change” SLOPE- 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 run change in x

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

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

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Find a positive slope Let (x 1, y 1 ) = (–4, 2) = (x 2, y 2 ) = (2, 6). m = y 2 – y 1 x 2 – x 1 6 – 2 2 – (– 4) = = 4 6 2 3 = Simplify. Substitute. Write formula for slope. Find the slope of the line shown.

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

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

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(0, 6) and (5, –4) m = y 2 – y 1 x 2 – x 1 Let (x 1, y 1 ) = (0, 6) and (x 2, y 2 ) = (5, – 4). – 4 – 6 5 – 0 = Write formula for slope. Substitute. Simplify. 10 5 = – = – 2 Find the slope of the line that passes through the points

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Find the slope of a horizontal and vertical line Find the slope of the line shown. Let (x 1, y 1 ) = (– 2, 4) and (x 2, y 2 ) = (4, 4). m = y 2 – y 1 x 2 – x 1 4 – 4 4 – (– 2) = 0 6 = = 0 Write formula for slope. Substitute. Simplify. EXAMPLE 4 Find the slope of the line shown. Let (x 1, y 1 ) = (3, 5) and (x 2, y 2 ) = (3, 1). m = y 2 – y 1 x 2 – x 1 Write formula for slope. 1 – 5 3 – 3 = Substitute. Division by zero is undefined. – 4 0 =

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Identifying Slopes m = y 2 – y 1 x 2 – x 1 Positive slope Negative slope Slope of 0 Undefined

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Rate of Change rate of change A rate of change compares a change in one quantity to change in another quantity. Example: hourly wage A rate of change describes how pay increases with respect to time spent working.

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The table shows the cost of using a computer at an Internet cafe for a given amount of time. Find the rate of change in cost with respect to time. Time(hours) 246 Cost (dollars)71421 Rate of change = change in cost change in time 14 –7 4 – 2 = 7 2 = 3.5 = The rate of change in cost is $3.50 per hour.

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Time(minute) 306090 Distance (miles) 1.534.5 The table shows the distance a person walks for exercise. Find the rate of change in distance with respect to time. Rate of change = change in distance change in time 3 – 1.5 60 – 30 = = 0.05 ANSWER The rate of change in distance is 0.05 mile / minute.

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Section 4.4 “Slopes of Lines” Section 4.4 “Slopes of Lines” How can you use algebra to describe the slope of a ramp? Complete the “Investigating Algebra Activity” on page 234 in your textbook. Complete the ‘Drawing Conclusions’ questions #1-6.

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What Did We Learn? Slope Rate of change m = y 2 – y 1 x 2 – x 1 rate of change A rate of change compares a change in one quantity to change in another quantity.

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Homework Text p. 239, #4-32 evens 24

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EXAMPLE 1 Find a positive slope Let (x 1, y 1 ) = (–4, 2) = (x 2, y 2 ) = (2, 6). m = y 2 – y 1 x 2 – x 1 6 – 2 2 – (–4) = = 4 6 2 3 = Simplify. Substitute.

EXAMPLE 1 Find a positive slope Let (x 1, y 1 ) = (–4, 2) = (x 2, y 2 ) = (2, 6). m = y 2 – y 1 x 2 – x 1 6 – 2 2 – (–4) = = 4 6 2 3 = Simplify. Substitute.

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