Question

A graph has number of days on the x-axis and number of canned goods on the y-axis. A line goes through points (2, 699) and (8, 321).
Nicholas volunteers at a local soup kitchen and he notices how quickly the kitchen is going through its stock of canned goods. Below is the graph representing the data Nicholas found.


Find the slope and y-intercept of the line.

m =
b =

Answer 1

To find the slope (m) and the y-intercept (b) of the line that passes through the points (2, 699) and (8, 321), we can use the formula for the slope of a line, which is given by

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

where \((x_1, y_1)\) and \((x_2, y_2)\) are the two points. Here, we can designate:

- Point 1: \((2, 699)\) → \((x_1, y_1) = (2, 699)\)
- Point 2: \((8, 321)\) → \((x_2, y_2) = (8, 321)\)

Now, substituting these values into the slope formula:

\[
m = \frac{321 - 699}{8 - 2} = \frac{-378}{6} = -63
\]

So, the slope \(m\) is:

\[
m = -63
\]

Next, to find the y-intercept (b), we can use the slope-intercept form of the equation of a line:

\[
y = mx + b
\]

We can use one of the points, such as (2, 699), and substitute \(m\) and the coordinates into the equation to solve for \(b\):

\[
699 = -63(2) + b
\]

Calculating the right-hand side:

\[
699 = -126 + b
\]

Now, solving for \(b\):

\[
b = 699 + 126 = 825
\]

Thus, the y-intercept \(b\) is:

\[
b = 825
\]

In summary, the slope and y-intercept of the line are:

\[
m = -63
\]
\[
b = 825
\]