3-3 Rate of change and Slope

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Presentation transcript:

3-3 Rate of change and Slope Rise over Run The change of the rise over the change of the run 𝒙 𝒚

A quick review Solve 2x – 5 = 25 Solve 52 – 6 = 3x -8 Sovle 6x + 3 = 6x -2 Solve 9 – 4x = 1 – 4x

A quick review x y (x,y) The equation P = 3000 – 22.5n represents the amount of profit P a catering company earns depending on the number of gusts n. After how many guests will the catering company make no profit? x y (x,y)

A quick review/Slope Graph y = -4x + 5 where does the graph cross the x-axis? EQ: Why are graphs useful? I will be able to: …. Use rate of change to solve problems …. Find the slope of a line. New Vocabulary Rate of change Slope

Important Information https://www.youtube.com/watch?v=ei3ASO9PEmc To determine if slope is positive or negative, look at the line from left to right (just like you read). Down …negative. UP…positive. x = any number Is always a vertical line. horizontal line Vertical line Y = any number Is always a horizontal line. This is considered undefined or no slope The slope is zero

Some examples Find Rate of Change CELL PHONE The table shows how the cost changes with the number of minutes used. Use the table to find the rate of change. Explain the meaning of the rate of change. DRIVING TIME Use the table to find the rate of change. Explain the meaning of the rate of change. .

Some more examples years millions of passports A. TRAVEL The graph to the right shows the number of U.S. passports issued in 2002, 2004, and 2006. Find the rates of change for 2002–2004 and 2004–2006. years millions of passports How are the different rates of change shown on the graph? Explain the meaning of the rate of change in each case.

Some more examples Explain the meaning of the slope in each case. How are the different rates of change shown on the graph? A. Airlines The graph shows the number of airplane departures in the United States in recent years. Find the rates of change for 1995–2000 and 2000–2005.

Some more examples Constant Rate of Change A. Determine whether the function is linear. Explain. B. Determine whether the function is linear. Explain. B. Determine whether the function is linear. Explain. A. Determine whether the function is linear. Explain.

Some more facts. Find the slope of the line that passes through (- 3, 2) and (4, 4,) Fine the slope of the line that passes through (-3, -4) and (-2, -8).

Some more examples Find the slope of the line that passes through (-3, 4) and (4,4) Find the slope of the line that passes through (4,5) and (7,6) Find the slope of the line that passes through (-3, 5) and (-2, -7) Find the slope of the line that passes through (-3, -1) and (5,-1)

Some more examples Find the slope of the line that passes through (-2, -4) and (-2,-3) Find the slope of the line that passes through (5, -1) and (5, -3)

Some more examples Find the value of r so that the line through (6,3) and (r,2) has a slope of 𝟏 𝟐 Find the value of p so that the line through (p,4) and (3, 1) has a slope of 𝟓 𝟖