Question

here is the equation and graph you got on the last slide: equation: y = -\frac{1}{2}x + 7.5 what does the slope mean in the context of this problem? based on your equation, how much snow was on the ground before it started melting? if this trend continues, how much snow would be left after 9 hours?

Explanation:

Step1: Interpret slope meaning

The equation is in slope - intercept form $y = mx + b$ where $m$ is the slope. Here $m=-\frac{1}{2}$. In the context of snow - melting, the slope represents the rate of change of the amount of snow on the ground. A slope of $-\frac{1}{2}$ means that the amount of snow on the ground decreases by $\frac{1}{2}$ inch per hour.

Step2: Find initial snow amount

The $y$ - intercept $b$ in the equation $y = mx + b$ gives the initial value. When $x = 0$ (before it started melting), substituting into $y=-\frac{1}{2}x + 7.5$, we get $y = 7.5$ inches.

Step3: Find snow amount after 9 hours

Substitute $x = 9$ into the equation $y=-\frac{1}{2}x + 7.5$. So $y=-\frac{1}{2}\times9 + 7.5=-4.5 + 7.5 = 3$ inches.

Answer:

1. The slope means the amount of snow on the ground decreases by $\frac{1}{2}$ inch per hour.
2. There were 7.5 inches of snow on the ground before it started melting.
3. There would be 3 inches of snow left after 9 hours.