Rate of Change and Slope

Warm Up

Determine if a rate of change is constant or variable. Find the rate of change, or the slope, from the graph of a proportional relationship. Use a table to determine if the rate of change is constant or variable. Use a graph to find the rate of change. Find the slope of a line using its graph. Connect the constant of proportionality to the rate of change, or slope, of a proportional relationship in equation form. Understand that the graph of a proportional relationship must be a line that passes through the origin and that the rate of change must be constant. This will facilitate the connection between the unit rate in a proportional relationship and the slope of its graph.

Draw the lines that connects the points from the tables in a coordinate plane and find the slope of the lines. Discuss how the graphs and their slopes are similar and how they are different.

Rate of Change and Slope To find the rate of change, or slope, find the ratio of the change in y values to the corresponding change in x values in tables or graphs. 𝑚= 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1 A linear relationship expresses a constant rate of change, called the slope. The rate of change can also be described as 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑑𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑡 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑖𝑛𝑑𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑡 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒 where x represents the independent variable, and y represents the dependent variable.

How do you know from the signs of the rise and run if a slope is positive or negative? The rules for dividing integers gives us this answer. If the rise and run have the same sine, the slope will be positive since the quotient of integers with the same sign is positive. If the rise and run have different signs, then the slope will be negative since the quotient of integers with different signs is negative.

A graph that rises from left to right has a positive slope A graph that falls from left to right has a negative slope. A horizontal line has a slope of 0. A vertical line has an undefined slope. Positive Negative Zero Undefined

The table shows the prices for various electronics during a storewide sale. Each item has the same percent discount. Complete the table and graph the points from the table. Then find the slope of the line connecting the points and give the percent discount.

Ben and Phoebe are finding the slope of a line Ben and Phoebe are finding the slope of a line. Ben chose two points on the line and used them to find the slope. Phoebe used two different points to find the slope. Did they get the same answer? Explain.

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