Question

diego is painting the walls of his house. he paints 8 square meters every hour. the graph shows the number of square meters of the house he paints over time. find the slope of this line. what does the slope mean in this situation? slope = \frac{vertical distance}{horizontal distance} = 8. options: every 8 hours, he paints 8 more square meters. every hour, he paints 8 more square meters. every 8 hours he paints 1 more square meter.

Explanation:

Step1: Identify slope formula

The slope formula is $m=\frac{y_2-y_1}{x_2-x_1}$, where $(x_1,y_1)$ and $(x_2,y_2)$ are points on the line.

Step2: Plug in given points

Use points $(2,16)$ and $(5,40)$:
$m=\frac{40-16}{5-2}=\frac{24}{3}=8$

Step3: Interpret the slope

The x-axis is hours, y-axis is square meters. Slope = $\frac{\text{square meters}}{\text{hours}}$, so it represents the painting rate per hour.

Answer:

Slope value: $8$
Correct interpretation: Every hour, he paints 8 more square meters.