Name Date Period Interpreting the Effects of Changing Slope and Y-intercept (6f) Slope tells you: Y-intercept tells you: Example: Sam works as a bicycle courier. She earns $10.00 for each delivery plus $0.75 for each ounce the package she delivers weighs. The graph of her pay is shown below. What would it mean if the slope of the graph where doubled? Original Slope: Slope doubled: What does it mean if slope of graph was doubled: 1. What would it mean if the slope of the function were changed to zero? 2. What would it mean if the slope of the function were negative? Example: Melinda is driving home at a speed of 80 kilometers per hour. Her distance from home is shown on the graph below. What would it mean if the y-intercept of the graph were increased by 40? Original Y-intercept: New Y-intercept: What does it mean if the y-intercept was increased by 40?
3. If the y-intercept were halved, how would the total amount of time it takes Melinda to get home be effected? 4. Ronnie drives home at a speed of 75 kilometers per hour from a distance of 300 kilometers away. Graph this situation and describe how the graph compares to the graph in Example 2 in terms of its slope and y-intercept. 5. Gwyneth s school holds a fundraiser to benefit organizations treating diabetes patients. For each student who participates in the fundraiser, the school donates $10. In addition, the students obtain a pledge of $7 from each donor they find. The graph of Gwyneth s contribution in terms of the number of donors she finds is shown below. If the contribution of each donor were increased to $9, how would the graph change? a. The slope would increase, causing the line to rise more steeply. b. The line would cross the y-axis at (0, 9) rather than (0, 10). c. The line would cross the x-axis at (9, 0). d. The slope would decrease, causing the line to rise less steaply. 6. The line graphed below represents the elevation of a car as it drives down a hill. What would be the meaning if the slop of the line were doubled? a. The hill would be twice as tall. b. The hill would be half as tall. c. The car would be moving twice as fast. d. The car would be moving half as fast.
7. A phone company charges $30.00 per month plus $0.10 for every minute of long distance phone calls. The total charge is graphed below. Which of the following would increase the charge per long distance minute to $0.20? a. Halving the y-intercept b. Doubling the y-intercept c. Halving the slope d. Doubling the slope 8. Each month, Rebecca adds money to her bank account. The amount of money in Rebecca s bank account is graphed below. If the y-intercept of this graph were changed to 75, what would change in the situation? a. Rebecca would have added $75 more to her bank account each month. b. Rebecca would have started with $75 more in her bank account. c. Rebecca would have started with $25 less in her bank account. d. Rebecca would have added $25 less to her bank account each month.
Meanings of Slope and Intercept (6b) Slope represents the. Example: Alejandro is stuffing envelopes for a political campaign. On Tuesday, he stuffed 4800 envelopes in 4 hours. On Wednesday, he stuffed 6000 envelopes in 5 hours. Draw a graph showing the relationship between the number of envelopes stuffed and time, and find its slope. Describe the meaning of the slope of your graph. Slope (show your work): Meaning of Slope: 1. Andrew can type 400 words in 5 minutes. He can type 1200 words in 15 minutes. Draw a graph representing this situation. Then find the slope and explain what it means. Slope: Meaning of Slope: 2. Find the slope of the graph below and describe its meaning. Slope: Meaning of Slope:
The y-intercept is The x-intercept is Example: At the beginning of each school year. Principal Sao stocks the teachers supply closet with new erasers. The graph below shows the change in number of erasers in the supply closet over time. The relationship can be represented by the equation intercept means in the context of the problem. Use the graph.. Find the x- and y-intercepts of the graph. Explain what each Y-intercept: Meaning: X-intercept: Meaning: 3. The graph below represents the relationship between the time and temperature of a solution during a chemical reaction. Find the x- and y-intercepts and explain what they mean in the situation. Y-intercept: Meaning: X-intercept: Meaning: 4. The equation represents the relationship between total score on a quiz, t, and questions counted incorrect, x. Find the intercepts of the equation and explain what they mean in the situation. Y-intercept: Meaning: X-intercept: Meaning:
5. The line segments of the graph shows the wages earned by a cashier during a week. Which of the following best describes the slope of the line segment? a. The cashier earns $6 per hour b. The cashier earns $6.25 per hour c. The cashier earns $12 per hour d. The cashier earns $12.50 per hour 6. The graph shows the height of a candle as it burns. Which of the following best describes the y-intercept? a. The height of the candle before it burned was 16 inches. b. The height of the candle after it burned was 2 inches. c. The candle burned in 5 hours. d. The candle burned at a rate of 3 inches per minute. 7. The graph shows the altitude of a car as a driver descends a mountain. What is the meaning of x-intercept? a. The height at which the driver started was 1500 ft. b. The height at which the driver stopped was 6 feet above sea level. c. The driver descended at 300 ft an hour. d. The driver reached the base of the mountain after 6 hours. 8. Some students collected the data below. They will graph the data. What will the slope for the graph represent? a. The change in average temperature per day. b. The change in average temperature per month. c. The high temperature for the sampling period. d. The range of temperatures for the sampling period.