Question

The number of gallons of water in the swimming pool x minutes after turning on the faucet is represented by y = 24x + 285.

a. Graph the linear equation.

b. interpret the slope and the y-intercept.

c.is the x-intercept applicable to the problem? Explain.

Answer 1

Given statement: The number of gallons of water in the swimming pool x minutes after turning on the faucet is represented by :

`y = 24x + 285` .....[1]

The equation of straight line is represented by
`y =mx+b` .....[2]

where

m represents the slope of line

and

b is the y-intercepts.

On comparing the equation [1] with [2] we get;

slope(m) = 24 and

y-intercept(b) = 285.

x-intercept defined as the graph crosses the x-axis i.e,

substitute the value of y =0 in [1] to solve for x;

0= 24x + 285

Subtract 285 from both sides we get;

-285 = 24x

Divide both sides by 24 we get;

`x = -(285)/(24) = -11.875`

x = -11.875

(a)

y= 24x + 285 where x is in minute.

You can see the graph of the equation as shown below.

(b)

Slope of the equation = 24

y-intercepts = 285

(c)

Since, x intercept is not applicable to this problem because value of x is negative as x represents the time(in minutes)