Question

the following data represent the weight (in grams) of various candy bars and the corresponding number of calories. candy bar a bar b bar c bar d bar e weight, x 49.1 55.5 46 51.5 57.5 calories, y 306.2 339 312 316 341 candy bar f bar g bar h bar i bar j weight, x 47.4 62.5 59.1 64 60.1 calories, y 318.8 349 350.2 348 327.2 (c) find the equation of the line that passes through (46.3,12) and (64,348) in slope - intercept form. y = y = 2x+220 (d) graph the line on the scatter diagram from part (a). choose the correct graph below. a. graph with x - weight and y - calories b. graph with x - weight and y - calories c. graph with x - weight and y - calories d. graph with x - weight and y - calories (e) use the linear equation you found in part (c) to predict the number of calories in a candy bar that weighs 50.9 grams. □ calories (f) interpret the slope of the line found in part (c). if the weight of the candy bar is increased by 1 gram, then the number of calories will increase by □ calories

Explanation:

Answer:

We are given the linear - equation $y = 2x+220$.

(c)

The slope - intercept form of a line is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. Given two points $(x_1,y_1)=(46.3,12)$ and $(x_2,y_2)=(64,348)$.
The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{348 - 12}{64 - 46.3}=\frac{336}{17.7}\approx18.983$. Using the point - slope form $y - y_1=m(x - x_1)$ with $(x_1,y_1)=(46.3,12)$ and $m\approx18.983$:

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If we assume the equation $y = 2x+220$ is correct (from the problem statement), the slope $m = 2$ and the y - intercept $b = 220$.

(d)

To graph the line $y = 2x+220$, we can find two points on the line.
Step1: Find the y - intercept point
When $x = 0$, $y=2\times0 + 220=220$. So one point is $(0,220)$.
Step2: Find another point
Let $x = 10$, then $y=2\times10+220=20 + 220=240$. So another point is $(10,240)$. Plot these two points on the scatter - diagram and draw a straight line through them.

(e)

We have the linear equation $y = 2x+220$. When $x = 50.9$, we substitute $x$ into the equation:

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(f)

The slope of the line $y = 2x+220$ is $m = 2$. This means that if the weight of the candy bar ($x$) is increased by 1 gram, then the number of calories ($y$) will increase by 2 calories.