Question

homework: applications of linear relationships

1. jeremy is paying his dad back for money that he borrowed to pay for a car repair. the amount that he owes his dad is shown in the graph.

what is the slope?
what does the slope represent in the situation?
what is the y-intercept?
what does the y-intercept represent in the situation?
equation:
graph with x-axis labeled months (1 - 10) and y-axis labeled amount owed ($) (100 - 1000), line plotted

1. chanel is reading an assigned book for her history class. the graph below shows the number of pages remaining in the book based on the number of hours she has spent reading.

what is the slope?
what does the slope represent in the situation?
what is the y-intercept?
what does the y-intercept represent in the situation?
equation:
graph with x-axis labeled hours (1 - 10) and y-axis labeled pages remaining (20 - 200), line plotted

1. a cabin charges renters a cost per night plus a fee for cleaning. the table below shows the cost of renting the cabin based on the number of nights. which of the following is a true statement?

what is the slope?
what does the slope represent in the situation?
what is the y-intercept?
what does the y-intercept represent in the situation?
equation:
table with # nights (0, 2, 4, 6) and total cost ($) (75, 325, 575, 825)

Explanation:

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Problem 1: Jeremy's Debt

Step1: Identify 2 points on graph

Points: $(0, 700)$ and $(9, 0)$

Step2: Calculate slope

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{0-700}{9-0}=-\frac{700}{9}\approx-77.78$

Step3: Interpret slope

Negative slope = monthly payment amount

Step4: Identify y-intercept

Y-intercept is $y$ at $x=0$: $(0,700)$

Step5: Interpret y-intercept

Initial amount borrowed from dad

Step6: Write linear equation

Use $y=mx+b$: $y=-\frac{700}{9}x+700$

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Problem 2: Chanel's Reading

Step1: Identify 2 points on graph

Points: $(0, 180)$ and $(3, 60)$

Step2: Calculate slope

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{60-180}{3-0}=-40$

Step3: Interpret slope

Negative slope = pages read per hour

Step4: Identify y-intercept

Y-intercept is $y$ at $x=0$: $(0,180)$

Step5: Interpret y-intercept

Total pages in the assigned book

Step6: Write linear equation

Use $y=mx+b$: $y=-40x+180$

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Problem 3: Cabin Rental

Step1: Identify 2 points from table

Points: $(0, 75)$ and $(2, 325)$

Step2: Calculate slope

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{325-75}{2-0}=125$

Step3: Interpret slope

Positive slope = cost per night

Step4: Identify y-intercept

Y-intercept is $y$ at $x=0$: $(0,75)$

Step5: Interpret y-intercept

One-time cleaning fee

Step6: Write linear equation

Use $y=mx+b$: $y=125x+75$

Answer:

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Problem 1:

1. Slope: $-\frac{700}{9}$ or approximately $-77.78$
2. Slope represents: Monthly payment to dad
3. Y-intercept: $700$
4. Y-intercept represents: Initial amount Jeremy borrowed
5. Equation: $y=-\frac{700}{9}x+700$

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Problem 2:

1. Slope: $-40$
2. Slope represents: Pages Chanel reads per hour
3. Y-intercept: $180$
4. Y-intercept represents: Total pages in the book
5. Equation: $y=-40x+180$

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Problem 3:

1. Slope: $125$
2. Slope represents: Cost per night for the cabin
3. Y-intercept: $75$
4. Y-intercept represents: One-time cleaning fee
5. Equation: $y=125x+75$