Question

use the graph to write an equation of the line.
hot air balloon
height (meters)
time (minutes)
interpret the slope.

Explanation:

Step1: Find the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(8,540)$ and $(x_2,y_2)=(25,200)$. Then $m=\frac{200 - 540}{25 - 8}=\frac{- 340}{17}=-20$.

Step2: Find the y - intercept $b$

Use the point - slope form $y - y_1=m(x - x_1)$ with the point $(8,540)$ and $m=-20$. So $y - 540=-20(x - 8)$. Expand to get $y-540=-20x + 160$. Then $y=-20x+700$.

Answer:

$y=-20x + 700$

The slope of $- 20$ means that the height of the hot - air balloon decreases by 20 meters per minute.