Question

the graph shows the relationship between the price of frozen yogurt and the number of ounces of frozen yogurt sold at different stores and restaurants. cost of frozen yogurt (graph with cost ($) on y - axis from 1 to 10 and size (oz) on x - axis from 2 to 20, and a line of best fit with data points). according to the line of best fit, about how many ounces of frozen yogurt can someone purchase for $5? options: 1.5, 2, 13, 15.5

Explanation:

Step1: Identify the line of best fit

The line of best fit is the straight line that represents the trend of the data points. We can see from the graph that it's a positive - sloped line.

Step2: Locate $y = 5$ on the y - axis

The y - axis represents the cost in dollars. We find the point on the line of best fit where the y - value (cost) is 5.

Step3: Find the corresponding x - value

The x - axis represents the size in ounces. When we look at the line of best fit, when $y = 5$ (cost is $5$), we trace horizontally to the line and then vertically down to the x - axis. From the graph, we can estimate that the x - value (number of ounces) is around 13. We can also calculate the slope of the line of best fit. Let's take two points on the line, for example, when $x = 4$, $y = 2$ and when $x = 8$, $y = 3$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{3 - 2}{8 - 4}=\frac{1}{4}=0.25$. The equation of the line is $y=mx + b$. Since when $x = 0$, $y = 0$ (the line passes through the origin), $b = 0$. So the equation is $y = 0.25x$. If $y = 5$, then $5=0.25x$, and $x=\frac{5}{0.25}=20$? Wait, no, maybe my two - point selection was wrong. Let's take another pair. When $x = 8$, $y = 3$, so $3 = m\times8$, so $m=\frac{3}{8}=0.375$. Then if $y = 5$, $x=\frac{5}{0.375}\approx13.33$, which is approximately 13.

Answer:

13