Bell Work Graph the equation y=2x+4. (Hint: Use a function table to determine the ordered pairs.)

Objective Learn to determine the slope of a line and recognize constant and variable rates of change.

Vocabulary Slope – the measure of the steepness of a line. slope = ______ = _________________ Rate of Change – the ratio of two quantities that change. (i.e. slope)

The slope of a line is a measure of its steepness and is the ratio of rise to run: y If a line rises from left to right, its slope is positive. If a line falls from left to right, its slope negative. x Run Rise Slope

Tell whether the slope is positive or negative. Then find the slope. The line rises from left to right. The slope is positive. Slope

Tell whether the slope is positive or negative. Then find the slope. The rise is 3. The run is 3. slope = rise run = 3333 =1 3 3 Slope

Tell whether the slope is positive or negative. Then find the slope. The line falls from right to left. The slope is negative –2 y x Slope

Tell whether the slope is positive or negative. Then find the slope. The rise is 2. The run is -3. slope = rise run = –2 y x Slope

The line does not point upward or downward so it is not positive or negative. Tell whether the slope is positive or negative. Then find the slope. Hmmmm….

The rise is 0. The run is 2. slope = rise run = 0202 =0 M(1, –1) N(3, –1) ‏ 2 Tell whether the slope is positive or negative. Then find the slope. Hmmmm….

You can graph a line if you know its slope and one of its points. Notes

Use the slope  and the point (1, –1) to graph the line 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 ● ● Slope and a Point

Use the slope and the point (–1, –1) to graph the line 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 ● Slope and a Point

Use the slope – and the point (2, 0) to graph the line 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 ● ● Slope and a Point

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. Rate of Change

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. Constant or Variable?

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 Constant or Variable?

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. Butterflies