Applications of Slope and Intercept

1. B. The number of seconds that passed before the printer started printing pages

What does the $x$-intercept represent?

The $x$-intercept tells us the value of the $x$-variable when the $y$-variable equals $0$.

In this context, $x$ represents the seconds since sending the print job, and $y$ represents how many pages have printed. So the $x$-intercept $(5, 0)$ 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. B. $x$-intercept

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.

3. D. None of the above

What does the $y$-intercept represent?

The $y$-intercept tells us the value of the $y$-variable when the $x$-variable equals $0$.

In this context, $x$ represents the number of tire rotations, and $y$ represents the distance past the tree. So the $y$-intercept at $(0, -15)$ says after $0$ tire rotations, Coleman was $15$ meters away from the tree and the tree was in front of him.

The Answer

The $y$-intercept represents the distance Coleman was away the tree when he started traveling.

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

4. A. Slope

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 many times the metronome clicks per bar. Since $x$ represents the number of bars of music he played, we are looking for how much $y$ (metronome clicks) changes when $x$ (bars played) increases by $1$.

The Answer

Slope represents how many times the metronome clicks per bar.