Applications of Slope and Intercept

1. A.

The wrestler gained weight each month, so we expect to have a positive slope.

The wrestler weighed $79.5$ when he started his diet, so we expect a positive $y$-intercept.

Based on this description, we expect a positive slope and a positive $y$-intercept.

2. D. $x$-intercept and $y$-intercept

To describe a point on the graph, we need a corresponding $(x,y)$.

In our case, these are corresponding values of hours of reading and number of pages left to read.

$\text { hours reading}$ $\text { pages left}$

                       ↓    ↓

                     $(x,  y)$

To describe the slope of the graph, we need information about the rate of change of the relationship.

In our case, this is the rate at which the number of pages left to read changes over time (in pages per hour).

Conrad has $180$ pages left when he has read for $0$ hours. This corresponds to the point $(0,180)$ and is a $y$-intercept.

It took Conrad $6$ hours to have $0$ pages left to read. This corresponds to the point $(6, 0)$ and is an $x$-intercept.

The $x$-intercept and $y$-intercept are given.

3. B.

Nour's altitude increases after driving awhile, so we expect to have a positive slope.

Nour starts below sea level, so we expect a negative $y$-intercept.

Based on this description, we expect a positive slope and a negative $y$-intercept.

4. C. Slope and a point that is not an intercept

To describe a point on the graph, we need a corresponding $(x,y)$ pair.

In our case, these are corresponding values of hours of painting and area left to paint.

$\text { hours of painting}$ $\text { area left}$

                              ↓    ↓

                            $(x,  y)$

To describe the slope of the graph, we need information about the rate of change of the relationship.

In our case, this is the rate at which the area left to paint changes over time (in square meters per hour).

Hiro painted his room at a rate of $8$ square meters per hour. This corresponds to a slope of $-8$.

After $3$ hours of painting, Hiro had $28$ square meters left to paint. This corresponds to the point $(3, 28)$ and is not an intercept.

The slope and a point that is not an intercept are given.

5. B.

The profit increases with each ticket, so we expect to have a positive slope.

They had to sell a few tickets just to cover production costs (to bring their profit from a negative value up to $0$), so we expect a positive xxx-intercept.

Based on this description, we expect a positive slope and a positive $x$-intercept.

6. A. Slope and $x$-intercept

To describe a point on the graph, we need a corresponding $(x,y)$ pair.

In our case, these are corresponding values of number of tickets sold and net profit.

$\text { tickets sold}$ $\text { net profit}$

                   ↓    ↓

                $(x,  y)$

To describe the slope of the graph, we need information about the rate of change of the relationship.

In our case, this is the rate at which the net profit changes per ticket sold (in dollars per ticket).

The organization had to sell $18$ tickets to cover their production costs and bring their net profit from a negative value up to $$0$. This corresponds to the point $(18,0)$ and is an $x$-intercept.

They sold each ticket for $$45$. This corresponds to a slope of $45$.

The slope and $x$-intercept are given.

7. D.

Mr. Mole descends each minute, so we expect to have a negative slope.

Mr. Mole starts below the ground, so we expect a negative $y$-intercept.

Based on this description, we expect a negative slope and a negative $y$-intercept.