Question

exit ticket
5 state your assumption the surface of grand lake is at an elevation of 648 feet. during a drought, the water level drops at a rate of 3 inches per day. write an equation in slope - intercept form that gives the elevation in feet y of the surface of grand lake after x days. explain any assumptions you made to write the equation.

Explanation:

Step1: Convert the rate to feet

Since 1 foot = 12 inches, 3 inches = $\frac{3}{12}=\frac{1}{4}$ feet per day. The rate of change (slope) is negative because the water - level is dropping. So, $m =-\frac{1}{4}$.

Step2: Identify the initial value

The initial elevation of the lake surface is 648 feet. So, the y - intercept $b = 648$.

Step3: Write the slope - intercept form equation

The slope - intercept form of a linear equation is $y=mx + b$. Substituting $m =-\frac{1}{4}$ and $b = 648$ into the equation, we get $y=-\frac{1}{4}x + 648$.
The assumption made is that the rate of water - level drop is constant throughout the drought. There are no external factors (such as sudden heavy rainfall, water being added from other sources, or changes in the rate due to geological factors) that affect the water - level drop during the period of $x$ days.

Answer:

The equation is $y =-\frac{1}{4}x+648$. The assumption is that the rate of water - level drop is constant during the drought and there are no external factors affecting the water level.