Question

the amount of snow on the ground is being measured on a warm day. after 3 hours there is 6 inches of snow on the ground. after 5 hours there is 5 inches of snow on the ground. write an equation to represent how much snow is left on the ground since the beginning of the day. what is the slope? m = what is the y - intercept? y=mx + b final answer what is the equation of the line? y =

Explanation:

Step1: Recall slope - formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $x$ be the number of hours and $y$ be the amount of snow. We have the points $(3,6)$ and $(5,5)$.
$m=\frac{5 - 6}{5 - 3}$

Step2: Calculate the slope

$m=\frac{-1}{2}=-\frac{1}{2}$

Step3: Use point - slope form to find y - intercept

The point - slope form is $y - y_1=m(x - x_1)$. Using the point $(3,6)$ and $m =-\frac{1}{2}$, we have $y - 6=-\frac{1}{2}(x - 3)$.
Expand to get $y-6=-\frac{1}{2}x+\frac{3}{2}$.
Add 6 to both sides: $y=-\frac{1}{2}x+\frac{3}{2}+6=-\frac{1}{2}x+\frac{3 + 12}{2}=-\frac{1}{2}x+\frac{15}{2}$. So the y - intercept $b=\frac{15}{2}$.

Answer:

Slope: $m =-\frac{1}{2}$
Y - intercept: $b=\frac{15}{2}$
Equation of the line: $y =-\frac{1}{2}x+\frac{15}{2}$