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Rate of change and slope

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cathyguyer

Rate of change allows you to quantify the relationship between two changing quantities by calculating the ratio of change in one quantity to the change in the other. It can be found using tables of data by taking the difference in the dependent variable and dividing by the difference in the independent variable. Rate of change can also be found using a graph by choosing two points and calculating the ratio of the change between them. Slope is another term for rate of change and can be found using the points on a graph or using the slope-intercept form of a linear equation.

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Rate of Change and Slope
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 =
Finding Rate of Change Using a Table Step 1: Find the difference in the dependent variable for two pairs of data. Step 2: Find the difference in the independent variable for the same two pairs of data. Step 3: Write the change in dependent over the change in independent as a ratio in simplest form. *The ratio is the rate of change! $120 5 $105 4 $90 3 $75 2 $60 1 Rental Charge Number of Days
Finding Rate of Change Using a Graph 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. Step 1: Choose two points from the graph. Step 2: Follow same procedure from above to find change of rate. 2000 1000 0 60 120 180
200 100 0 1 2 3 4 5 6 Time (hours)
Finding Slope Using Points Slope = EX: (5, 7) (-2, 1)
Find Slope: (2, 5) (4, 7) B. (-1, 4) (3, -2)
Slope-Intercept Form The slope-intercept form of a linear equation is y = mx + b where m is the slope and b is the y-intercept. y = 3x + 5 slope = 3 y-intercept = +5
y = -2x +1 y = 遜 x 3 y = 7x Write the equation: Slope = 5, y-intercept = -9 Slope = -4, y-intercept = 2 Slope = 他, y-intercept = 0
Graphing An Equation Graph y = 3x + 1 Step 1: identify the y-intercept and graph that point (0, 1) Step 2: Use the slope (rise over run (3/1)) to graph several more points. Step 3: Connect the points to create the line.
Assignment: Pg. Odd numbers only.

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Rate of change and slope

  • 1. Rate of Change and Slope
  • 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. Finding Rate of Change Using a Table Step 1: Find the difference in the dependent variable for two pairs of data. Step 2: Find the difference in the independent variable for the same two pairs of data. Step 3: Write the change in dependent over the change in independent as a ratio in simplest form. *The ratio is the rate of change! $120 5 $105 4 $90 3 $75 2 $60 1 Rental Charge Number of Days
  • 4. Finding Rate of Change Using a Graph 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. Step 1: Choose two points from the graph. Step 2: Follow same procedure from above to find change of rate. 2000 1000 0 60 120 180
  • 5. 200 100 0 1 2 3 4 5 6 Time (hours)
  • 6. Finding Slope Using Points Slope = EX: (5, 7) (-2, 1)
  • 7. Find Slope: (2, 5) (4, 7) B. (-1, 4) (3, -2)
  • 8. Slope-Intercept Form The slope-intercept form of a linear equation is y = mx + b where m is the slope and b is the y-intercept. y = 3x + 5 slope = 3 y-intercept = +5
  • 9. y = -2x +1 y = 遜 x 3 y = 7x Write the equation: Slope = 5, y-intercept = -9 Slope = -4, y-intercept = 2 Slope = 他, y-intercept = 0
  • 10. Graphing An Equation Graph y = 3x + 1 Step 1: identify the y-intercept and graph that point (0, 1) Step 2: Use the slope (rise over run (3/1)) to graph several more points. Step 3: Connect the points to create the line.
  • 11. Assignment: Pg. Odd numbers only.