Practice with the Slope of a Line

1. Beatrice graphed the relationship between the time (in seconds) since she sent a print job to the printer and the number of pages printed.

   
   

   What does the \(x\)-intercept represent in this context

   Choose 1 answer:
   

   1. The number of pages already printed when Beatrice sent the job
   2. The number of seconds that passed before the printer started printing pages
   3. The number of pages printed per second

   4. None of the above

2. An observation point was originally in line with the top of a waterfall, but the waterfall moves a constant distance each year from erosion. The following graph shows the relationship between the time since ‍1998 and the distance the top of the waterfall is from the observation point. Negative years represent time before 1998.

   
   

   What feature of the graph represents the distance from the observation point in 2003?

   Choose 1 answer:

   1. Slope
   2. \(x\)-intercept
   3. \(y\)-intercept

   4. None of the above

3. Madhavi scoops a bowlful of cereal out of a container that has a mix of oat and wheat cereal pieces. She graphed the relationship between the possible masses of oat and wheat cereal in her bowl.

   
   

   What does the \(y\)-intercept represent in this context?

   Choose 1 answer:

   1. The mass of the cereal if it is all oat pieces
   2. The mass per piece of wheat cereal
   3. The mass per piece of oat cereal

   4. None of the above

4. Nirmala graphed the relationship between the duration (in hours) of using an oil lamp and the volume (in milliliters) of oil remaining.

   
   

   What feature of the graph represents how long Nirmala can use the lamp before it runs out of oil?

   Choose 1 answer:

   1. Slope
   2. \(x\)-intercept
   3. \(y\)-intercept
   4. None of the above

Source: Khan Academy, https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs/x2f8bb11595b61c86:applying-intercepts-and-slope/e/using-slope-intercepts
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.

1. The ‍\(x\)-intercept tells us the value of the ‍\(x\)-variable when the ‍\(y\)-variable equals.

   In this context, \(x\) represents the seconds since sending the print job, and ‍\(y\) represents how many pages have printed. So the \(x\)-intercept at (5, 0) says that when ‍5 seconds had passed, there were 0 pages printed.

   
   

   The answer

   The \(x\)-intercept represents the number of seconds that passed before the printer started printing pages.

2. What does each feature tell us?

   The \(x\)-intercept tells us the value of the ‍\(x\)-variable when the ‍\(y\) variable equals 0.

   The \(y\)-intercept tells us the value of the ‍\(y\)-variable when the ‍\(x\) variable equals 0.

   The slope tells us how much the \(y\)-variable changes for each ‍1-unit increase in the \(x\)-variable.

   What feature do we need?

   We want to know the distance from the observation point in 2003. Since ‍\(y\) represents the distance from the observation point, we are looking for the value of ‍\(y\) (the distance) when ‍\(x=5\) (because ‍2003 is ‍5 years after 1998).

   Answer

   The point (5, 2.55) represents the distance from the observation point in 2003.

   Since that was not an option, the answer is none of the above.

3. What does the \(y\)-intercept represent?

   The \(y\)-intercept tells us the value of the ‍\(y\)-variable when the ‍\(x\)-variable equals.

   In this context, \(x\) represents the mass of the wheat cereal, and ‍\(y\) represents the mass of the oat cereal. So the ‍\(y\)-intercept at approximately ‍(0, 28) says that if the bowl has ‍0 grams of wheat cereal, it has about 28 grams of oat cereal.

   
   

   The answer 

   The \(y\)-intercept represents the mass of the cereal if it is all oat pieces.

4. What does each feature tell us?

   The \(x\)-intercept tells us the value of the ‍\(x\)-variable when the ‍\(y\) variable equals 0.

   The \(y\)-intercept tells us the value of the ‍\(y\)-variable when the ‍\(x\) variable equals 0.

   The slope tells us how much the \(y\)-variable changes for each ‍1-unit increase in the \(x\)-variable.

   What feature do we need?

   We want to know how long Nirmala can use the lamp before it runs out of oil. Since ‍\(y\) represents the volume of oil, we are looking for the value of ‍\(x\) (the duration) when ‍\(y=0\) (when the lamp has no oil).

   Answer

   The ‍\(x\)-intercept represents how long Nirmala can use the lamp before it runs out of oil.