Practice with the Slope of a Line
buttons.Practice Problems
Answers
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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.
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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.
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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.
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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.