Question

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? Correct equation: The slope is . The y-intercept is . In days, the water level will be 26 feet.

Answer 1

w= -0.5d+34
The slope is -0.5 as the water I receding by .05 feet per days (d). The y-intercept is 34 as you start with 34 feet of water.

To find how many days it'll take for the water level to reach 26 feet you'll plug 26 in for w in this equation and then solve.

26= -0.5d +34
-8 = -0.5d
Minus 34 from both sides to get the slope alone. (As shown above.) Then divide by -0.5 to get d on it's own as shown below.
16 = d

It should take 16 days for the water to recede from 34 feet to 26 feet. You can plug 16 into the original equation to check your work.

Answer 2

$slope (m) = -0.5$ (represents the rate at which the water level decreases per day)

$y-intercept (b) = 34$ (this represents the initial water level of the river)

The correct equation is $w = -0.5d + 34$

The number of days for the water level to get to 26 feet is 16 days.

Given:

• Water level of river = 34 ft (initial value/y-intercept)
• Rate of change = -0.5 ft per day (slope)

• If,

w = water level after, d = days,

the equation in slope-intercept form can be expressed as:

$w = md + b$

• Where,

$slope (m) = -0.5$ (this implies the rate at which the water level decreases per day)

$y-intercept (b) = 34$ (this represents the initial water level of the river)

To write the equation, substitute $m = -0.5 and b = 34$ into  $w = md+ b$.

Thus:

$w = -0.5d + 34$

• To find the number of days it will take the water level to reduce to 26 ft, substitute w = 26 into $w = -0.5d + 34$.

• Thus:

$26= -0.5d + 34\\\\26 -34 = -0.5d + 34 - 34\\\\-8 = -0.5d$

Divide both sides by -0.5

$16 = d\\\\d = 16$

• In 16 days, the water level will get to 26 feet.

In conclusion,

• $slope (m) = -0.5$ (represents the rate at which the water level decreases per day)
• $y-intercept (b) = 34$ (this represents the initial water level of the river)
• The correct equation is $w = -0.5d + 34$
• The number of days for the water level to get to 26 feet is 16 days.

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