Question

1. a.where is the y-intercept on this graph? b. if we talk for 0 minutes, how much do we owe c. what is the slope of this line, or rate? d. what would the slope represent in real life? graph: cell phone graph with x-axis labeled minutes (0–10) and y-axis labeled with cost ($0, $0.10, $0.20, ..., $1.30), points plotted on the grid

Explanation:

Part A

Step1: Recall y - intercept definition

The y - intercept is the point where the graph intersects the y - axis, which occurs when \(x = 0\).
From the graph, when \(x=0\) (minutes = 0), the \(y\) - value (cost) is \(\$0\). So the y - intercept is at the point \((0,0)\) or when \(x = 0\), \(y=0\).

Part B

Step1: Interpret \(x = 0\) in context

When we talk for 0 minutes (\(x = 0\)), we look at the y - value (the amount owed) at \(x = 0\). From the graph, at \(x = 0\) (0 minutes of talk time), the cost (amount owed) is \(\$0\).

Part C

Step1: Recall slope formula

The slope \(m\) of a line is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\), where \((x_1,y_1)\) and \((x_2,y_2)\) are two points on the line.
Let's take two points from the graph. For example, when \(x_1 = 0,y_1 = 0\) and \(x_2=1,y_2 = 0.10\) (assuming the y - axis is in dollars, and the first non - zero point is at \(x = 1,y=\$0.10\)).

Step2: Calculate slope

Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0.10 - 0}{1 - 0}=\frac{0.10}{1}=0.10\). So the slope (rate) is \(\$0.10\) per minute.

Part D

Answer:

The slope represents the rate of change of the cost with respect to the time spent talking on the cell phone. In real - life terms, since the slope is \(\$0.10\) per minute, it represents the cost per minute of talking on the cell phone. For each additional minute of talk time, the amount owed (cost) increases by \(\$0.10\).

Part A Answer: The y - intercept is at \((0,0)\) (or when minutes = 0, cost = \(\$0\))

Part B Answer: If we talk for 0 minutes, we owe \(\$0\)

Part C Answer: The slope (rate) is \(\$0.10\) per minute

Part D Answer: The slope represents the cost per minute of talking on the cell phone (the amount the cost increases per minute of talk time)