Question

the following data represent the weight (in grams) of a box of raisins and the number of raisins in the box.
weight, w | number of raisins, n
42.4 | 87
42.1 | 82
42.6 | 86
42.5 | 86
42.8 | 91
42.8 | 94
42.4 | 89
42.5 | 86
42.3 | 87
42.7 | 89
(a) no/yes option, with no selected
(b) draw a scatter plot of the data treating weight as the independent variable. choose the correct answer below options a, b, c, d with scatter plots, c selected
(c) find the equation of the line containing the points (42.3, 82) and (42.8, 94).
n = \square (use integers or decimals for any numbers in the expression)

Explanation:

Step1: Calculate the slope

The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \( x_1 = 42.3 \), \( y_1 = 82 \), \( x_2 = 42.8 \), \( y_2 = 94 \). So \( m=\frac{94 - 82}{42.8 - 42.3}=\frac{12}{0.5} = 24 \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Using the point \((42.3, 82)\) and \( m = 24 \), we have \( N-82 = 24(w - 42.3) \).
Expand the right - hand side: \( N-82=24w-24\times42.3 \). Calculate \( 24\times42.3 = 1015.2 \). Then \( N=24w-1015.2 + 82 \).
Simplify the constant term: \( - 1015.2+82=-933.2 \). So \( N = 24w-933.2 \). We can also use the other point to verify. Let's substitute \( w = 42.8 \) into the equation: \( N=24\times42.8-933.2=1027.2 - 933.2 = 94 \), which matches the \( y \) - value of the second point.

Answer:

\( N = 24w-933.2 \)