Question

what does the slope of the line tell you about the situation? jade gained 100 pounds every month. jade gained 200 pounds every month. jade gained 100 pounds every 3 months. jade gained 200 pounds every 3 months.

Explanation:

Step1: Identify two points on the line

From the graph, when \( x = 0 \) (age = 0 months), \( y = 200 \) pounds. When \( x = 3 \) (age = 3 months), \( y = 300 \) pounds.

Step2: Calculate the slope

The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Substituting the points \((0, 200)\) and \((3, 300)\), we get \( m=\frac{300 - 200}{3 - 0}=\frac{100}{3} \) pounds per month? Wait, no, wait. Wait, the change in \( y \) (weight) from \( x = 0 \) to \( x = 3 \) is \( 300 - 200 = 100 \) pounds, and the change in \( x \) (months) is \( 3 - 0 = 3 \) months. Wait, no, wait, maybe I misread. Wait, when \( x = 0 \), \( y = 200 \); when \( x = 3 \), \( y = 300 \). So the change in weight is \( 300 - 200 = 100 \) pounds over \( 3 - 0 = 3 \) months? No, that can't be. Wait, no, maybe another point. Wait, when \( x = 0 \), \( y = 200 \); when \( x = 3 \), \( y = 300 \). So the slope is \( \frac{300 - 200}{3 - 0}=\frac{100}{3}\approx33.33 \) pounds per month? But the options are about every 3 months. Wait, let's check the options. The options are about gain per month or per 3 months. Let's see the change in weight over 3 months. From \( x = 0 \) to \( x = 3 \), weight goes from 200 to 300, so gain of 100 pounds in 3 months. So that's 100 pounds every 3 months. Wait, let's verify with another point. When \( x = 6 \), \( y = 400 \). From \( x = 3 \) (300 pounds) to \( x = 6 \) (400 pounds), that's also 100 pounds in 3 months. So the slope (rate of change) is 100 pounds every 3 months.

Answer:

Jade gained 100 pounds every 3 months.