Question

A local public library decides to track the number of hours that a certain computer is being used. The table represents the number of hours, y, which is dependent on the number of days, x.

x
y
3
21
5
37
7
53

What is the linear equation that represents this situation?
y = 8 x + 45
y = 8 x minus 3
y = 2 x + 16
y = 2 x minus 32

Answer 1

To find the linear equation that represents the relationship between the number of days (x) and the number of hours (y), we can use the given data points to determine the slope and the y-intercept.

We have the following data points:

- (3, 21)
- (5, 37)
- (7, 53)

First, we can calculate the slope \( m \) using any two points. Let's use the points (3, 21) and (5, 37):

The formula for slope \( m \) is:

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

Substituting the values from the points:

\[
m = \frac{37 - 21}{5 - 3} = \frac{16}{2} = 8
\]

Next, we can use the slope and one of the points to find the y-intercept \( b \) using the equation of a line in the form \( y = mx + b \). We can use the point (3, 21):

\[
21 = 8(3) + b
\]
\[
21 = 24 + b
\]
\[
b = 21 - 24
\]
\[
b = -3
\]

Thus, the equation of the line is:

\[
y = 8x - 3
\]

So, the correct linear equation that represents this situation is:

**y = 8x - 3**.