Use the slope-intercept form of the equation of a line to model the situation. The slope is -0.2 inches per day (since the slope corresponds to the rate of change), and the y-intercept is 54 inches (since the y-intercept corresponds to the initial value at day 0).
The equation of a line with slope m and y-intercept b is:
[tex]y=mx+b[/tex]
Replace m=-0.2 and b=54:
[tex]y=-0.2x+54[/tex]
Notice that y represents the depth of the pond and x the number of days. Substitute x=20 to find the depth of the pond after 20 days:
[tex]\begin{gathered} y=-0.2(20)+54 \\ =-4+54 \\ =50 \end{gathered}[/tex]
Therefore, the depth of the pond after 20 days is 50 inches.
