Question

this graph shows a proportional relationship.

what is the unit rate shown by the graph?
1.25 minutes per word 1.25 words per minute
75 minutes per word 75 words per minute

Explanation:

Step1: Recall unit rate for proportional graph

For a proportional relationship \( y = kx \) (where \( y \) is words, \( x \) is time), unit rate \( k=\frac{y}{x} \). We can pick a point from the graph. Let's take when \( x = 4 \) minutes, \( y = 300 \) words (from the grid: at \( x = 4 \), \( y \) is 300).

Step2: Calculate unit rate

Using \( k=\frac{y}{x} \), substitute \( y = 300 \), \( x = 4 \). So \( k=\frac{300}{4}=75 \). This means 75 words per minute (since \( y \) is words, \( x \) is minutes, so rate is words per minute). Also, check the options: "75 minutes per word" is incorrect (rate should be words per minute, not minutes per word for writing speed), 1.25 is too low. So the unit rate is 75 words per minute.

Answer:

75 words per minute