Graphing Linear Equations Unit Test

Question

17 of 1817 of 18 Items

Question
Use the image to answer the question.

A graph shows a horizontal axis representing time in weeks ranging from 0 to 10 in increments of 1. The vertical axis represents number of books read ranging from 0 to 10 in increments of 1. Two plotted points are: left parenthesis 0 comma 5 right parenthesis, left parenthesis 5 comma 8 right parenthesis. These points are joined by a straight line with arrows on both the ends.

Interpret the slope in the context of this situation. Give the most simplified rate using whole numbers.

(1 point)
Responses

Someone had 5 weeks to read a book.
Someone had 5 weeks to read a book.

Someone read 5 books in a week.
Someone read 5 books in a week.

Someone reads 3 books every 5 weeks.
Someone reads 3 books every 5 weeks.

Someone is reading 5 books every 3 weeks.

Answer 1

To find the slope of the line that connects the two points (0, 5) and (5, 8), we can use the formula for slope (m):

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

Substituting the coordinates of the points:

• \((x_1, y_1) = (0, 5)\)
• \((x_2, y_2) = (5, 8)\)

So,

\[ m = \frac{8 - 5}{5 - 0} = \frac{3}{5} \]

The slope of \(\frac{3}{5}\) means that for every 5 weeks, the number of books read increases by 3.

In the context of the situation, this means:

Someone reads 3 books every 5 weeks.

Therefore, the correct response is:

Someone reads 3 books every 5 weeks.