Question

the following data represent the weight (in grams) of a box of raisins and the number of raisins in the box.

(c) find the equation of the line containing the points, $(42.3,82)$ and $(42.8,94)$
$n=$

Explanation:

Step1: Calculate the slope \(m\)

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(42.3,82)\) and \((x_2,y_2)=(42.8,94)\).

$$m=\frac{94 - 82}{42.8 - 42.3}=\frac{12}{0.5}=24$$

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

Using the point \((x_1,y_1)=(42.3,82)\) and \(m = 24\), we have \(N-82=24(w - 42.3)\).
Expand the equation: \(N-82=24w-24\times42.3\).
\(24\times42.3 = 1015.2\), so \(N-82=24w - 1015.2\).
Then \(N=24w-1015.2 + 82\).
\(N=24w-933.2\)

Answer:

\(N = 24w-933.2\)