Unit 3, Lesson 9
Slopes Don't Have to Be Positive
Grade 8
9.1
Warm-up
Which three go together? Why do they go together?
4 lines plotted on a grid, lines labeled a,b,c,d. line a, positive slope, intersects line d. line d, negative slope, intersects lines a, b, c. line b, positive slope, intersects lines d and c. line c, positive slope, intersects lines b and d.
9.3
Activity
This graph shows the amount of money in dollars that is on Han’s fare card for every day of last July.
- Describe what happened with the money on Han’s fare card in July.
- Plot and label 3 different points on the line.
- Write an equation where represents the day in July and represents the dollars on the card.
- What value makes sense for the slope of the line that represents the money on Han’s fare card in July?
Student Lesson Summary
At the end of winter in Maine, the snow on the ground was 30 inches deep. Then there was a particularly warm day and the snow melted at the rate of 1 inch per hour. The graph shows the relationship between the time since the snow started to melt and the depth of the remaining snow.
Graphs with a negative slope often describe situations where some quantity is decreasing over time.
Since the depth of the snow decreases by 1 inch per hour, the rate of change is -1 inch per hour and the slope of this graph is -1. The vertical intercept is 30 since the snow was 30 inches high before it started to melt.
graph on grid, origin O. horizontal axis, time since snow started to melt in hours, scale 0 to 11, by 1's. vertical axis, depth of snow in inches, scale 0 to 30, by 5's. line with negative slope drawn that goes through points 2 comma 28, 3 comma 27. triangle with down 1 right 1 drawn below these 2 points. line also goes through 5 comma 25 and 10 comma 20. triangle with down 5 right 5 drawn below these 2 points.
Graphs with a slope of 0 describe situations where there is no change in the -value even though the -value is changing.
graph on a grid, origin O. horizontal axis, time since winning contest in days, scale 0 to 11, by 1's. vertical axis, balance on fare card in dollars, 0 to 6, by 1's. horizontal line through 2 days comma 5 dollars and 5 days comma 5 dollars.
For example, Elena wins a prize that gives her free bus rides for a year. Her fare card already had $5 on it when she won the prize. Here is a graph of the amount of money on her fare card after winning the prize. Since she doesn’t need to add or use money from her fare card for the next year, the amount on her fare card will not change. The rate of change is 0 dollars per day and the slope of this graph is 0. All graphs of linear relationships with slopes of 0 are horizontal.
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