3.3 Rate of Change and Slope Algebra 1

Objectives Essential Question Use rate of change to solve problems. Find the slope of a line. Essential Question How do I find the slope of a table, graph, or points?

Equation:

Example 1 Find Rate of Change DRIVING TIME Use the table to find the rate of change. Explain the meaning of the rate of change. m = 38 Notice: Each time x increases by 2 hours, y increases by 76 miles. Answer: This means the car is traveling at a rate of 38 miles per hour.

Constant change in x and y!!! Example 2 Constant Rate of Change A. Determine whether the function is linear. Explain. If so, find the slope. Constant change in x and y!!!

Example 3 Constant Rate of Change B. Determine whether the function is linear. Explain. If so, find the slope.

m = 𝟏 𝟐𝟎 Let’s Check! #1 Answer: This means that CELL PHONE - The table shows how the cost changes with the number of minutes used. Use the table to find the rate of change. Explain the meaning of the rate of change. m = 𝟏 𝟐𝟎 Answer: This means that for every 1 dollar spent, 20 minutes are used.

Let’s Check! #2 A. Determine whether the function is linear. Explain. Find the slope if it is positive. A. Yes, the rate of change is constant. Slope = 2/5 B. No, the rate of change is constant. Slope = 5. C. Yes, the rate of change is not constant. Slope = 5/2 D. No, the rate of change is not constant.

Let’s Check! #3 B. Determine whether the function is linear. Explain. Answer: No, the change in x is not constant.

Find the rate of change from a graph. Find the slope of each line.

Find the rate of change. Find the slope of the line.

Find the rate of change. Find the slope of the line.

Example 4 Variable Rate of Change A. TRAVEL The graph to the right shows the number of U.S. passports issued in 2002, 2004, and 2006. Find the rates of change for 2002–2004 and 2004–2006. millions of passports years Answer: Rate of change from 2002-2004 = 950,000 Rate of change from 2004-2006 = 1,600,000

Example 4B B. Explain the meaning of the rate of change in each case. Variable Rate of Change B. Explain the meaning of the rate of change in each case. Answer: For 2002–2004, there was an average annual increase of 950,000 in passports issued. Between 2004 and 2006, there was an average yearly increase of 1,600,000 passports issued.

Let’s Check! #4 A. Airlines The graph shows the number of airplane departures in the United States in recent years. Find the rates of change for 1995–2000 and 2000–2005. Answer: Rate of change from 1995-2000 = 180,000 2000-2005 = 180,000

Finding Slope using the FORMULA!

Example 5 Positive, Negative, and Zero Slope A. Find the slope of the line that passes through (–3, 2) and (5, 5). m = 𝟑 𝟖 How about graphing it?

Example 6 Positive, Negative, and Zero Slope B. Find the slope of the line that passes through (–3, –4) and (–2, –8). m = −𝟒 𝟏 How about graphing it?

Example 7 Undefined Slope Find the slope of the line that passes through (–2, –4) and (–2, 3). m = 𝟕 𝟎 Undefined How about graphing it?

Let’s Check! #5 C. Find the slope of the line that passes through (–3, –1) and (5, –1). A. undefined B. 8 C. 2 D. 0

Let’s Check! #6 Find the slope of the line that passes through (3, –1) and (5, –3). m = −𝟐 𝟐 =−𝟏

Example 8 Find Coordinates Given the Slope Find the value of r so that the line through (6, 3) and (r, 2) has a slope of r = 4

Example 9 Find Coordinates Given the Slope Find the value of r so that the line through (2, 6) and (9, r) has a slope of 3. r = 27

Homework 3.3 P. 177 #1-7 and 12-13

Exit Slip – Write on a notecard