Question

Suppose the Rocky Mountains have 72 centimeters of snow. Warmer weather is melting the snow at a rate of

5.8 centimeters a day. If the snow continues to melt at this rate, after seven days of warm weather, how much
snow will be left?

Answer 1

31.4 cm

Explanation:

`\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}`

The y-intercept is the y-value when x is zero, so the initial value.

If the initial amount of snow is 72 cm, the y-intercept is 72.

The slope is the rate of change.

If the snow is melting at a rate of 5.8 cm per day, then the rate of change is -5.8.

Therefore, the equation that models the given word problem is:

`\boxed{\begin{minipage}{5.4 cm}\phantom{w}\\$y=-5.8x+72$\\\\where:\\ \phantom{ww}$\bullet$ $y$ is height of the snow in cm. \\ \phantom{ww}$\bullet$ $x$ is the time in days.\\\end{minipage}}`

To find how much snow is left after 7 days, substitute x = 7 into the found equation:

`\implies y=-5.8(7)+72`

`\implies y=-40.6+72`

`\implies y=31.4`

Therefore, there will be 31.4 cm of snow left after seven days of warm weather.