Question

the following data represent the weight (in grams) of various candy bars and the corresponding number of calories. (c) find the equation of the line that passes through (46.312) and (64.348) in slope - intercept form. y = 2x+220 (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. a. b. c. d. (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:

Step1: Identify the slope - intercept form

The general form of a linear equation is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. Given \(y = 2x+220\), here \(m = 2\) and \(b = 220\).

Step2: Interpret the slope

The slope \(m\) represents the rate of change of \(y\) with respect to \(x\). In the context of the problem, \(x\) is the weight of the candy bar in grams and \(y\) is the number of calories. So, when \(x\) changes by 1 unit (1 gram), \(y\) changes by \(m\) units. Since \(m = 2\), when the weight of the candy bar is increased by 1 gram, the number of calories increases by 2 calories.

Answer:

We are given the linear - equation \(y = 2x+220\).
(f) The slope of the line \(y = mx + b\) is \(m\). In the equation \(y = 2x+220\), the slope \(m = 2\). 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.