Understanding Slope

Show your work for each problem.

1.
What does slope measure?
1. a)The length of a line
2. b)The position of a line
3. c)The steepness of a line
4. d)The direction of a line
Answer: The steepness of a line
Slope measures how steep a line is - how much it rises or falls as you move from left to right.
2.
In the slope formula , what goes in the numerator?
1. a)The horizontal change (run)
2. b)The x-coordinate
3. c)The y-intercept
4. d)The vertical change (rise)
Answer: The vertical change (rise)
The rise (vertical change, or change in y) goes in the numerator (on top). The formula is .
3.
A line rises 6 units and runs 2 units. What is its slope?
Answer: 3
Slope . The line goes up 3 units for every 1 unit to the right.
4.
Find the slope of the line through and .
Answer: 3
5.
Find the slope of the line through and .
Answer: 2
1. What is ? 8
2. What is ? 4
3. What is the slope (rise/run)? 2
6.
Find the slope of the line through and .
Answer: -2
. The negative slope means the line goes down from left to right.
7.
A horizontal line has a slope of:
1. a)0
2. b)-1
3. c)Undefined
4. d)1
Answer: 0
A horizontal line has rise = 0. Slope = . No matter how far you go horizontally, you don't go up or down.
8.
A vertical line has a slope that is:
1. a)Undefined
2. b)Infinity
3. c)0
4. d)1
Answer: 0
A vertical line has run = 0. Slope = , which is undefined because you cannot divide by zero.
9.
Find the slope of the line through and .
Answer: -2
1. What is ? -12
2. What is ? 6
3. What is the slope? -2
10.
If a line goes downward from left to right, its slope is:
1. a)Negative
2. b)Positive
3. c)Undefined
4. d)Zero
Answer: Negative
When a line goes down from left to right, the change in y is negative while the change in x is positive. Negative divided by positive equals negative.
11.
A road rises 150 meters over a horizontal distance of 2500 meters. What is the grade as a percentage?
Answer: 6
1. What is the rise? 150
2. What is the run? 2500
3. Calculate rise/run as a decimal: 0.06
4. Convert to percentage (multiply by 100): 6
12.
Find the slope of the line through and .
Answer: 3
13.
The cost of a taxi ride is 5 euros for 0 km and 25 euros for 10 km. What is the rate in euros per km (the slope)?
Answer: 2
1. What is the change in cost (rise)? 20
2. What is the change in distance (run)? 10
3. What is the rate per km (slope)? 2
14.
What is the slope of a line passing through and ? (Enter 'undefined' if applicable)
Answer: undefined
The run is . Since we cannot divide by zero, the slope is undefined. This is a vertical line.
15.
A water tank is being filled. At 2 minutes, it has 15 liters. At 8 minutes, it has 45 liters. What is the filling rate (slope) in liters per minute?
Answer: 5
1. What is the change in volume (rise)? 30
2. What is the change in time (run)? 6
3. What is the filling rate (slope)? 5
16.
Which slope represents the steepest line?
1. a)
2. b)
3. c)
4. d)
Answer:
is the steepest because is the largest. A slope of 5 means the line rises 5 units for every 1 unit to the right.