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The equation P=28+2.54wmodels the relation between the amount of R and y's monthly water bill payment, P, in dollars, and the number of units of water, w, used.

(a) Find the payment for a month when R and y used 0 units of water.

(b) Find the payment for a month when R and y used 15 units of water.

(c) Intercept the slope and P-intercept of the equation.

(d) Graph the equation.

Short Answer

Expert verified

(a) Monthly payment is $28 for 0 units of water.

(b) Monthly payment is $66.1for 15 units of water.

(c) Slope is 2.54and 0,28is the P-intercept.

(d)

Step by step solution

01

Part (a). Step 1. Given information

The given equation isP=28+2.54w.

02

Part (a). Step 2. Substitute and simplify

  • Substitute 0 for w in the given equation and solve for P.

P=28+2.540=28

  • So, monthly payment is $28 when 0 units of water are used.

03

Part (b). Step 1. Substitute and simplify

  • Substitute 15 for w in the given equation and solve for P.

P=28+2.5415=28+38.1=66.1

  • So, monthly payment is $66.1 when 15 units of water are used.
04

Part (c). Step 1. Determine the slope and P-intercept.

  • The given equation is of the form y=mx+b. So, the slope is 2.54.
  • Substitute 0 for w in the given equation and obtain the value of P.

P=28+2.540=28

  • So, 0,28is the P-intercept.
05

Part (d). Step 1. Simplify the slope

  • Rewrite m=2.54in fractional form.

2.54=2.541

  • Multiply the numerator and denominator of the obtained fraction by 100.

2.54×100100=254100

06

Part (d). Step 2. Graph

  • From the point 0,28, go up 254 units and then move 100 units to the right to obtain the second point.
  • The second point will be 100,282.
  • Join the obtained points to plot the equation.

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