Question #13294295 - SAT Suite Question Bank

ID: 13294295

Modded SAT Question Bank by Abdullah Mallik

The graph shown models the number of candy bars a certain machine wraps with a label in $x$ seconds.

According to the graph, what is the estimated number of candy bars the machine wraps with a label per second?

$2$
$40$
$78$
$80$

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Correct Answer: B

Rationale

Choice B is correct. For the graph shown, the x-axis represents time, in seconds, and the y-axis represents the number of candy bars wrapped. The slope of a line in the xy-plane is the change in $y$ for each $1$ -unit increase in $x$ . It follows that the slope of the graph shown represents the estimated number of candy bars the machine wraps with a label per second. The slope, $m$ , of a line in the xy-plane can be found using any two points, $left parenthesis x 1 comma y 1 right parenthesis$ and $left parenthesis x 2 comma y 2 right parenthesis$ , on the line and the slope formula $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ . The graph shown passes through the points $left parenthesis 0 comma 0 right parenthesis$ and $left parenthesis 2 comma 80 right parenthesis$ . Substituting these points for $left parenthesis x 1 comma y 1 right parenthesis$ and $left parenthesis x 2 comma y 2 right parenthesis$ , respectively, in the slope formula yields $m = \frac{80 - 0}{2 - 0}$ , which is equivalent to $m = \frac{80}{2}$ , or $m equals 40$ . Therefore, the estimated number of candy bars the machine wraps with a label per second is $40$ .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.

Question Difficulty: Easy