Question

the following data represent the weight (in grams) of various candy bars and the corresponding number of calories.
(a) draw a scatter diagram of the data treating weight as the independent variable. choose the correct scatter diagram below.
(b) what type of relation appears to exist between the weight of a candy bar and the number of calories?

• linear
• nonlinear

(c) find the equation of the line that passes through (46,312) and (64,348) in slope - intercept form.
y=
(type an expression using x as the variable. use integers or decimals for any numbers in the expression.)
(d) graph the line on the scatter diagram from part (a). choose the correct graph below.

Explanation:

Answer:

(a) To draw the scatter - diagram, we plot the points with weight (x) on the x - axis and calories (y) on the y - axis. Looking at the data points:

Candy Bar	Weight (x)	Calories (y)
Bar B	55.5	339
Bar C	46	312
Bar D	51.5	316
Bar E	57.5	341
Bar F	47.4	318.8
Bar G	62.5	349
Bar H	59.1	350.2
Bar I	64	348
Bar J	60.1	327.2

We match these points to the scatter - diagrams given. By plotting these points, we can see that the correct scatter - diagram is the one that represents these data pairs accurately. Without actually plotting on graph paper, we can visually inspect the given scatter - diagrams and match the general pattern of points.

(b) By observing the scatter - diagram, we can see that the points seem to follow a linear pattern. As the weight of the candy bar (x) increases, the number of calories (y) also seems to increase in a somewhat straight - line fashion. So the type of relation is Linear.

(c) The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points \((x_1,y_1)=(46,312)\) and \((x_2,y_2)=(64,348)\)

Step1: Calculate the slope

$$m=\frac{348 - 312}{64 - 46}=\frac{36}{18}=2$$

Step2: Use the point - slope form \(y - y_1=m(x - x_1)\) to find the y - intercept

Using the point \((46,312)\) and \(m = 2\)

$$y-312=2(x - 46)$$

$$y-312=2x-92$$

$$y=2x + 220$$

(d) To graph the line \(y = 2x+220\) on the scatter - diagram:

• When \(x = 40\), \(y=2\times40 + 220=80 + 220=300\)
• When \(x = 70\), \(y=2\times70+220=140 + 220=360\)

We plot the points \((40,300)\) and \((70,360)\) and draw a straight line passing through them on the scatter - diagram.