Question

name:date: ____ per: ____homework 10: slope-intercept applications this is a 2-page document! 1. the enrollment of a school in 2000 was 1200. since then, it has increased at a rate of 35 students per year. write an equation to represent the enrollment of the school each year after 2000. identify your variables.a) what is the rate of change?b) what is the initial value?c) what is the independent variable?d) what is the dependent variable?2. the registration at a preschool is $125. then, parents must also pay $475 per month for tuition. write an equation to represent the total cost after each month. identify your variables.a) what is the rate of change?b) what is the initial value?c) what is the independent variable?d) what is the dependent variable?3. there are 18 gallons of gas in a car at the beginning of a trip. each hour into the trip, 2.5 gallons are used. write an equation to represent the gas left in the car after each hour into the trip. identify your variables.a) what is the rate of change?b) what is the initial value?c) what is the independent variable?d) what is the dependent variable?4. the taxi company charges $0.75 per mile driven in addition to a flat fee of $3.00. write an equation to represent the total cost for a taxi cab trip. identify your variables.a) what is the rate of change?b) what is the initial value?c) what is the independent variable?d) what is the dependent variable?

Explanation:

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Problem 1

Step1: Define variables

Let $x$ = number of years after 2000, $y$ = total enrollment

Step2: Write slope-intercept equation

Slope-intercept form: $y=mx+b$, where $m$ = rate of change, $b$ = initial value.
$y=35x+1200$

Step3: Answer sub-questions

a) Rate of change = slope ($m$)
b) Initial value = y-intercept ($b$)
c) Independent variable = input ($x$)
d) Dependent variable = output ($y$)

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Problem 2

Step1: Define variables

Let $x$ = number of months, $y$ = total cost

Step2: Write slope-intercept equation

$y=475x+125$

Step3: Answer sub-questions

a) Rate of change = slope ($m$)
b) Initial value = y-intercept ($b$)
c) Independent variable = input ($x$)
d) Dependent variable = output ($y$)

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Problem 3

Step1: Define variables

Let $x$ = number of hours into trip, $y$ = gas left (gallons)

Step2: Write slope-intercept equation

Gas decreases, so slope is negative: $y=-2.5x+18$

Step3: Answer sub-questions

a) Rate of change = slope ($m$)
b) Initial value = y-intercept ($b$)
c) Independent variable = input ($x$)
d) Dependent variable = output ($y$)

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Problem 4

Step1: Define variables

Let $x$ = number of miles driven, $y$ = total taxi cost

Step2: Write slope-intercept equation

$y=0.75x+3.00$

Step3: Answer sub-questions

a) Rate of change = slope ($m$)
b) Initial value = y-intercept ($b$)
c) Independent variable = input ($x$)
d) Dependent variable = output ($y$)

Answer:

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Problem 1

Equation: $y=35x+1200$
a) 35 students per year
b) 1200 students
c) Number of years after 2000
d) Total school enrollment

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Problem 2

Equation: $y=475x+125$
a) $\$475$ per month
b) $\$125$
c) Number of months
d) Total cost for preschool

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Problem 3

Equation: $y=-2.5x+18$
a) -2.5 gallons per hour
b) 18 gallons
c) Number of hours into the trip
d) Gallons of gas left in the car

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Problem 4

Equation: $y=0.75x+3.00$
a) $\$0.75$ per mile
b) $\$3.00$
c) Number of miles driven
d) Total cost of the taxi trip