Question

sam and his mother made an agreement for the upcoming weekend concerning internet usage and watching television. the function on the graph below represents the agreement they made.
internet and television
graph with x-axis: hours on internet, y-axis: hours watching television, line from (0,10) to (5,0)
if sam follows the agreement, what can be inferred from the slope of the graph above?
a. for every two hours sam does not spend watching television, he may use the internet for one hour.
b. for every two hours sam spends watching television, he may use the internet for one hour.
c. for every one hour sam does not spend watching television, he may use the internet for two hours.
d. for every one hour sam spends watching television, he may use the internet for two hours.

Explanation:

Step1: Identify two points on the line

The graph has points \((0, 10)\) (when \(x = 0\) hours on internet, \(y = 10\) hours watching TV) and \((5, 0)\) (when \(x = 5\) hours on internet, \(y = 0\) hours watching TV).

Step2: Calculate the slope

The slope \(m\) of a line through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting \((x_1, y_1)=(0, 10)\) and \((x_2, y_2)=(5, 0)\), we get \(m=\frac{0 - 10}{5 - 0}=\frac{- 10}{5}=-2\).

The slope of \(-2\) means that for every \(1\) unit increase in \(x\) (hours on internet), \(y\) (hours watching TV) decreases by \(2\) units. In other words, for every \(2\) hours decrease in television watching (not spending on TV), the internet usage increases by \(1\) hour. This matches option A.

Answer:

A. For every two hours Sam does not spend watching television, he may use the internet for one hour.