The water level of a river is 34 feet and is receding at a rate of 0.5 foot per day. Write an equation that represents the water level, w, after d days. Identify the slope and y-intercept and describe their meanings. In how many days will the water level be 26 feet?
To write the equation that represents the water level after d days, we can use the slope-intercept form of a linear equation, which is y = mx + b. In this case, y represents the water level, x represents the number of days, m represents the slope, and b represents the y-intercept.
The slope (m) represents the rate at which the water level is receding, which is given as -0.5 foot per day. Since the water level is decreasing, the slope should be negative. Therefore, the slope (m) in this case is -0.5.
The y-intercept (b) represents the initial water level, which is given as 34 feet. Since the y-intercept is the value of y when x (the number of days) is 0, the y-intercept (b) in this case is 34.
Putting these together, the equation that represents the water level (w) after d days is:
w = -0.5d + 34
To find the number of days it will take for the water level to be 26 feet, we can substitute 26 for w in the equation and solve for d:
26 = -0.5d + 34
-0.5d = 26 - 34
-0.5d = -8
d = -8 / -0.5
d = 16
Therefore, it will take 16 days for the water level to be 26 feet.