Do Now Graph the linear function. y = 2x + 4 Course Slope and Rates of Change Hwk: p 44

EQ: How do I determine the slope of a line and to recognize constant and variable rates of change? Course Slope and Rates of Change M7A3.a Plot points on a coordinate plane; M7A3.b Represent, describe, and analyze relations from tables, graphs, and formulas

Vocabulary slope Insert Lesson Title Here Course Slope and Rates of Change

The slope of a line is a measure of its steepness and is the ratio of rise to run: y If a line points downward as x increases, its slope is negative. If a line points upward as x increases, its slope is positive. x Run Rise Course Slope and Rates of Change

Tell whether the slope is positive or negative. Then find the slope. Additional Example 1A: Identifying the Slope of the Line Course Slope and Rates of Change The line rises from left to right. The slope is positive.

Tell whether the slope is positive or negative. Then find the slope. Additional Example 1A Continued The rise is 3. The run is 3. slope = rise run = 3333 =1 3 3 Course Slope and Rates of Change

Tell whether the slope is positive or negative. Then find the slope. Additional Example 1B: Identifying the Slope of the Line Course Slope and Rates of Change The line falls from right to left. The slope is negative –2 y x

Tell whether the slope is positive or negative. Then find the slope. Additional Example 1B Continued The rise is 2. The run is -3. slope = rise run = Course Slope and Rates of Change –2 y x

Check It Out: Example 1A The line does not point upward or downward so it is not positive or negative. Course Slope and Rates of Change Tell whether the slope is positive or negative. Then find the slope.

Check It Out: Example 1A Continued The rise is 0. The run is 2. slope = rise run = 0202 =0 M(1, –1) N(3, –1) 2 Course Slope and Rates of Change Tell whether the slope is positive or negative. Then find the slope.

Check It Out: Example 1B Insert Lesson Title Here (0, –4) (–2, 4) 8 –2 The rise is 8. The run is –2. slope = rise run = 8 –2 =–4 Tell whether the slope is positive or negative. Then find the slope. The line falls from left to right. The slope is negative. Course Slope and Rates of Change

You can graph a line if you know its slope and one of its points. Course Slope and Rates of Change

Use the slope  and the point (1, –1) to graph the line. Additional Example 2A: Using Slope and a Point to Graph a Line 2121 From point (1, 1) move 2 units down and 1 unit right, or move 2 units up and 1 unit left. Mark the point where you end up, and draw a line through the two points. y x – –2 = or rise run ● ● Course Slope and Rates of Change

Course Slope and Rates of Change You can write an integer as a fraction by putting the integer in the numerator of the fraction and a 1 in the denominator. Remember!

Use the slope and the point (–1, –1) to graph the line. Additional Example 2B: Using Slope and a Point to Graph a Line 1212 From point (–1, –1) move 1 unit up and 2 units right. Mark the point where you end up, and draw a line through the two points. y x – –2 = rise run 1 2 ● Course Slope and Rates of Change

Use the slope  and the point (2, 0) to graph the line. Check It Out: Example 2A 2323 From point (2, 0) move 2 units down and 3 units right, or move 2 units up and 3 unit left. Mark the point where you end up, and draw a line through the two points. y x – –2 = or rise run ● ● Course Slope and Rates of Change

Use the slope and the point (–2, 0) to graph the line. Check It Out: Example 2B 1414 From point (–2, 0) move 1 unit up and 4 units right. Mark the point where you end up, and draw a line through the two points. y x – –2 = rise run 1 4 ● Course Slope and Rates of Change

The ratio of two quantities that change, such as slope, is a rate of change. A constant rate of change describes changes of the same amount during equal intervals. A variable rate of change describes changes of a different amount during equal intervals. The graph of a constant rate of change is a line, and the graph of a variable rate of change is not a line. Course Slope and Rates of Change

Tell whether each graph shows a constant or variable rate of change. A.B. Additional Example 3: Identifying Rates of Change in Graphs The graph is nonlinear, so the rate of change is variable. The graph is linear, so the rate of change is constant. Course Slope and Rates of Change

Check It Out: Example 3 Insert Lesson Title Here Tell whether each graph shows a constant or variable rate of change. A.B. The graph is nonlinear, so the rate of change is variable. The graph is linear, so the rate of change is constant. y x – –2 y x – –2 Course Slope and Rates of Change

The graph shows the distance a monarch butterfly travels overtime. Tell whether the graph shows a constant or variable rate of change. Then find how fast the butterfly is traveling. Additional Example 4: Using Rate of Change to Solve Problems Course Slope and Rates of Change

Additional Example 4 Continued The graph is a line, so the butterfly is traveling at a constant rate of speed. The amount of distance is the rise, and the amount of time is the run. You can find the speed by finding the slope. slope (speed) = rise (distance) run (time) = 20miles 1 hour The butterfly travels at a rate of 20 miles per hour. Course Slope and Rates of Change

Check It Out: Example 4 The graph shows the distance a jogger travels over time. Is he traveling at a constant or variable rate. How fast is he traveling? Insert Lesson Title Here Time (min) Distance (mi) Time (min) Distance (mi) Course Slope and Rates of Change

Check It Out: Example 4 Continued Insert Lesson Title Here The graph is a line, so the jogger is traveling at a constant rate of speed. slope (speed) = rise (distance) run (time) = 1 mi 7 min The jogger travels at a rate of 1 mile every 7 minutes. The amount of distance is the rise, and the amount of time is the run. You can find the speed by finding the slope. Course Slope and Rates of Change

TOTD 1. Tell whether the slope is positive or negative. Then find the slope. Negative; -1 Insert Lesson Title Here Course Slope and Rates of Change

TOTD 2. Use the slope and the point (–2, –3) to graph the line. Insert Lesson Title Here 1212 Course Slope and Rates of Change

TOTD 3. Tell whether the graph shows a constant or variable rate of change. Insert Lesson Title Here Course Slope and Rates of Change variable