Question

1. ryan is writing a composition for homework. he decides to keep track of the number of sentences he writes compared to the time, in minutes, he works. the graph below show the data he collected.

a. at what rate does ryan write his composition?
b. what is the y-intercept?
ryans composition
sentences written
time (minutes)

Explanation:

Part a: Find the writing rate

Step 1: Recall the formula for rate (slope)

The rate at which Ryan writes is the slope of the line, calculated as \( \text{slope} = \frac{\text{change in } y}{\text{change in } x} \), where \( y \) is sentences written and \( x \) is time in minutes.

Step 2: Identify two points on the line

From the graph, when \( x = 20 \) minutes, \( y = 30 \) sentences; when \( x = 40 \) minutes, \( y = 60 \) sentences.

Step 3: Calculate the slope

Using the slope formula: \( \text{slope} = \frac{60 - 30}{40 - 20} = \frac{30}{20} = 1.5 \) sentences per minute.

Part b: Find the y - intercept

Step 1: Recall the definition of y - intercept

The y - intercept is the value of \( y \) when \( x = 0 \).

Step 2: Observe the graph

The line passes through the origin \((0,0)\), so when \( x = 0 \), \( y = 0 \).

Answer:

a. The rate at which Ryan writes his composition is \( 1.5 \) sentences per minute.
b. The y - intercept is \( 0 \).