Determine whether the following is a correct description of slope:
\dfrac{\text{Horizontal rise}}{\text{Vertical run}}
\dfrac{\text{Vertical rise}}{\text{Horizontal run}}
\dfrac{\text{Horizontal run}}{\text{Vertical rise}}
\dfrac{\text{Vertical run}}{\text{Horizontal rise}}
State the term used to the change in the horizontal distance along a line.
State the definiton of the slope of a line.
For each of the following segments containing A and B:
Find the rise going from A and B.
Find the run going from A and B.
Find the slope of the \overline{AB}.
A \left( - 4 , 0\right) and B \left(0, 2\right)
A \left(0, 4\right) and B \left(1, 0\right)
Identify what kind of slope the following lines have.
A line crosses the x-axis at 7, and crosses the y-axis at - 6.
Is the slope of the line positive or negative?
The slope of a line is \dfrac{3}{2}, and when x = 0, y = -1.
Determine whether the following could be the graph of the line:
A staircase is to be built so that its maximum steepness is 0.6.
If each step goes in 22 \text{ cm}, solve for the maximum height, in centimeters, it can rise vertically.
A paratrooper falls to the ground along a diagonal line. His fall begins 1157 \text{ m} above the ground, and the line he follows has a slope of 1.3. That is, he falls 1.3 \text{ m} vertically for every 1 \text{ m} he moves across horizontally.
How far horizontally across the ground does he land from his initial position in the sky?
Gas costs a certain amount per gallon. The following table shows the cost in dollars of various amounts of gas.
| \text{Number of gallons }(x) | 0 | 10 | 20 | 30 | 40 |
|---|---|---|---|---|---|
| \text{Cost of gas }(y) | 0 | 12.70 | 25.40 | 38.10 | 50.80 |
Write an equation linking the number of gallons of gas pumped \left( x \right) and the cost of the pgasetrol \left( y \right).
How much does gas cost per gallon?
How much would 73 gallons of gas cost at this unit price?
In the equation, y = 1.27 x, what does 1.27 represent?
A diver starts at the surface of the water and begins to descend below the surface at a constant rate. The following table shows the depth of the diver over 5 minutes.
| \text{Number of minutes passed }(x) | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| \text{Depth of diver in meters }(y) | 0 | 1.4 | 2.8 | 4.2 | 5.6 |
What is the increase in depth each minute?
Write an equation for the relationship between the number of minutes passed \left( x \right) and the depth \left( y \right) of the diver.
In the equation, y = 1.4 x, what does 1.4 represent?
At what depth would the diver be after 6 minutes?
How long does the diver take to reach 12.6 \text{ m} beneath the surface?
A dam used to supply water to the neighboring town had the following data recorded for its volume over a number of months.
| Month | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| Volume (billions of liters) | 134 | 117 | 100 | 83 |
At what rate is the volume of water in the dam changing?
Consider the proportional relationship shown in the graph, showing the number of fish caught over time.
What is the unit rate of this relationship in fraction?
Interpret your answer from part (a).
What feature of the straight line graph does the rate of change relate to?
David and Xavier are saving money for a vacation. David knows that he can represent his savings over time using the equation y = \dfrac{13}{2} x, where x represents the number of days and y represents the savings.
Xavier saves \$10 every 3 days.
Complete the table showing Xavier's savings over time.
| Days | ⬚ | 6 | 9 | 12 |
|---|---|---|---|---|
| Dollars saved | 10 | 20 | 30 | ⬚ |
Comparing the graphs of each person's savings, how can you tell who is saving more per day?
Using the graph, who has the greater rate of savings?
Two construction workers are competing to see who can lay the most bricks in one hour. The graph shows the number of bricks layed and the time, in minutes.
Interpret the rate of change of the given lines.
Determine who can lay more bricks in 60 minutes.
Explain why the y-intercept of both lines is 0.
Alicia has concluded that the rate of change is greater in f\left(x\right) than g\left(x\right) because it is higher on the given graph.
Explain and correct her error.
The following graph shows the distance Natalia swam during a recent open water swim:
What is the slope of the line?
What does the slope of the line represent in terms of the situation?
The following graph shows the number of batches of cookies produced in a factory:
What is the slope of the line?
What does the slope of the line represent in terms of the situation?