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1. Suppose that the water level of a river is 34 feet and that it is receding at a rate of 0.5 foot per day. Write an equation for the water level, y, after x days. In how many days will the water level be 26 feet?
Slope(m)=
y-intercept(b)=
equation y=
Answer=

Answer :

croissantart

Slope = -0.5

Y-intercept = 34

Equation:  y = -0.5x + 34

Answer = It will take 16 days for the water level to be 26 feet.

MrRoyal

The question is an illustration of a linear function.

  • The equation of the function is: [tex]\mathbf{y = 34- 0.5 x}[/tex]
  • The number of days to reach 26ft is 16

The given parameters are:

[tex]\mathbf{Level = 34ft}[/tex]

[tex]\mathbf{Rate = -0.5ft/day}[/tex]

The equation of the function is:

[tex]\mathbf{y = Level +Rate \times x}[/tex]

Where:

y represents the water level

x represents the number of days

So, we have:

[tex]\mathbf{y = 34- 0.5 \times x}[/tex]

[tex]\mathbf{y = 34- 0.5 x}[/tex]

A linear equation is represented as;

[tex]\mathbf{y = mx + b}[/tex]

So, by comparison:

[tex]\mathbf{Slope(m) = -0.5}[/tex]

[tex]\mathbf{y-intercept (b) = 34}[/tex]

When the water level is 26, it means y = 26.

So, we have:

[tex]\mathbf{y = 34- 0.5 x}[/tex]

[tex]\mathbf{26 = 34 - 0.5x}[/tex]

Collect like terms

[tex]\mathbf{26 - 34= - 0.5x}[/tex]

[tex]\mathbf{-8= - 0.5x}[/tex]

Divide both sides by -0.5

[tex]\mathbf{16= x}[/tex]

Rewrite as:

[tex]\mathbf{x = 16}[/tex]

Hence, the number of days to reach 26ft is 16

Read more about linear functions at:

https://brainly.com/question/20286983

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