Question

b. what do the vertical and horizontal intercepts, and mean in this situation?

Explanation:

Step1: Recall definition of intercepts

The vertical - intercept is the point where the line crosses the vertical (y - axis) and the horizontal - intercept is the point where the line crosses the horizontal (x - axis).

Step2: Identify vertical intercept

The line crosses the vertical axis at the point where the number of packs of cards is 0. Looking at the graph, when the number of packs of cards (x - value) is 0, the number of sheets of stickers (y - value) is 6. So the vertical intercept is 6.

Step3: Identify horizontal intercept

The line crosses the horizontal axis at the point where the number of sheets of stickers is 0. To find this, we can first find the equation of the line. The slope $m$ between two points $(x_1,y_1)=(0,6)$ and $(x_2,y_2)=(7,8)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{8 - 6}{7-0}=\frac{2}{7}$. Using the point - slope form $y - y_1=m(x - x_1)$ with $(x_1,y_1)=(0,6)$, the equation of the line is $y=\frac{2}{7}x + 6$. When $y = 0$, we have $0=\frac{2}{7}x+6$, then $\frac{2}{7}x=-6$, and $x=-21$. But in the context of this real - world situation (non - negative values for packs of cards and sheets of stickers), we can also note that if we assume the line continues in the positive x - direction, we can use the two points $(0,6)$ and $(7,8)$ to find when $y = 0$. The line has a positive slope, and if we consider the trend, we can work backwards. The change in y from $(7,8)$ to $(0,6)$ is a decrease of 2 when x decreases by 7. To get from $y = 6$ to $y = 0$ (a decrease of 6), the decrease in x is $6\div2\times7 = 21$. Since we are in the non - negative x - region, we can say that in the context of the graph shown (assuming non - negative values for both variables), the horizontal intercept is not applicable in the positive x - domain. If we consider the mathematical line, the horizontal intercept is $x=-21$. But in the context of the real - world situation (number of packs of cards can't be negative), we say the horizontal intercept does not exist in the context of the given situation.
The vertical intercept represents the number of sheets of stickers when no packs of cards are bought. It means that there are 6 sheets of stickers initially (even when no cards are purchased). Since there is no point where the line crosses the positive x - axis in the context of the real - world situation (non - negative number of packs of cards), the horizontal intercept has no meaning in this context.

Answer:

The vertical intercept is 6. The horizontal intercept does not exist in the context of the real - world situation (non - negative number of packs of cards).