Rate of change and slope

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A ppt reviewing how to find slope and rate of change.

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Rate of change and slope

  1. 1. Rate of Change and Slope
  2. 2. Rate of Change allows you to see the relationship between two quantities that are changing (like; number of text messages and amount of bill. Or number of baskets made and basketball score) Rate of change =
  3. 3. Finding Rate of Change Using a Table <ul><li>Step 1: Find the difference in the dependent variable for two pairs of data. </li></ul><ul><li>Step 2: Find the difference in the independent variable for the same two pairs of data. </li></ul><ul><li>Step 3: Write the change in dependent over the change in independent as a ratio in simplest form. </li></ul><ul><li>*The ratio is the rate of change! </li></ul>$120 5 $105 4 $90 3 $75 2 $60 1 Rental Charge Number of Days
  4. 4. Finding Rate of Change Using a Graph <ul><li>The graph shows the altitude of an airplane as it comes in for a landing. Find the rate of change. Explain what this rate of change means. </li></ul><ul><li>Step 1: Choose two points from the graph. </li></ul><ul><li>Step 2: Follow same procedure from above to find change of rate. </li></ul>2000 1000 0 60 120 180
  5. 5. <ul><li>200 </li></ul><ul><li>100 </li></ul><ul><li>0 </li></ul><ul><li>1 2 3 4 5 6 </li></ul><ul><li>Time (hours) </li></ul>
  6. 6. Finding Slope Using Points <ul><li>Slope = </li></ul><ul><li>EX: (5, 7) (-2, 1) </li></ul>
  7. 7. <ul><li>Find Slope: </li></ul><ul><li>(2, 5) (4, 7) </li></ul><ul><li>B. (-1, 4) (3, -2) </li></ul>
  8. 8. Slope-Intercept Form <ul><li>The slope-intercept form of a linear equation is y = mx + b where m is the slope and b is the y-intercept. </li></ul><ul><li>y = 3x + 5 slope = 3 </li></ul><ul><li>y-intercept = +5 </li></ul>
  9. 9. <ul><li>y = -2x +1 </li></ul><ul><li>y = ½ x – 3 </li></ul><ul><li>y = 7x </li></ul><ul><li>Write the equation: </li></ul><ul><li>Slope = 5, y-intercept = -9 </li></ul><ul><li>Slope = -4, y-intercept = 2 </li></ul><ul><li>Slope = ¾, y-intercept = 0 </li></ul>
  10. 10. Graphing An Equation <ul><li>Graph y = 3x + 1 </li></ul><ul><li>Step 1: identify the y-intercept and graph that point (0, 1) </li></ul><ul><li>Step 2: Use the slope (rise over run (3/1)) to graph several more points. </li></ul><ul><li>Step 3: Connect the points to create the line. </li></ul>
  11. 11. <ul><li>Assignment: Pg. </li></ul><ul><li>Odd numbers only. </li></ul>

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