Question

name hour quiz october 28, 2025: linear equations, line of best fit & translations part #1: use the tables below to write the equation of the line and answer each question: you bought a car and its value is depreciating. you opened a savings account and are depositing money into it. find the slope: slope = find the slope: slope = find the y - intercept: y - int = find the y - intercept: y - int = write the equation and explain its meaning in detail: write the equation and explain its meaning in detail: what is the car worth in 10 years? answer = what is the savings account at in 2 years? (12 months = 1 year) answer =

Explanation:

Step1: Calculate the slope for the car value

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(2,68700)\) and \((x_2,y_2)=(5,58200)\).

$$m=\frac{58200 - 68700}{5 - 2}=\frac{-10500}{3}=-3500$$

Step2: Find the \(y -\)intercept for the car value

Use the point - slope form \(y - y_1=m(x - x_1)\). Using \((x_1,y_1)=(2,68700)\) and \(m=-3500\)

$$y-68700=-3500(x - 2)$$

$$y-68700=-3500x+7000$$

$$y=-3500x + 75700$$

The \(y -\)intercept \(b = 75700\)

Step3: Calculate the value of the car in 10 years

Substitute \(x = 10\) into \(y=-3500x + 75700\)

$$y=-3500\times10+75700=-35000 + 75700=40700$$

Step4: Calculate the slope for the savings account

Let \((x_1,y_1)=(3,3375)\) and \((x_2,y_2)=(7,4675)\)

$$m=\frac{4675 - 3375}{7 - 3}=\frac{1300}{4}=325$$

Step5: Find the \(y -\)intercept for the savings account

Use the point - slope form \(y - y_1=m(x - x_1)\). Using \((x_1,y_1)=(3,3375)\) and \(m = 325\)

$$y-3375=325(x - 3)$$

$$y-3375=325x-975$$

$$y=325x+2400$$

The \(y -\)intercept \(b = 2400\)

Step6: Calculate the savings account value in 2 years (24 months)

Substitute \(x = 24\) into \(y=325x+2400\)

$$y=325\times24+2400=7800 + 2400=10200$$

Answer:

• For the car:
• SLOPE \(=-3500\)
• Y - Int \(=75700\)
• Equation: \(y=-3500x + 75700\), where \(x\) is the number of years since buying the car and \(y\) is the value of the car. The slope \(-3500\) means the car depreciates by \(\$3500\) per year and the \(y -\)intercept \(75700\) is the initial value of the car when \(x = 0\) (at the time of purchase).
• ANSWER \(=\$40700\)
• For the savings account:
• SLOPE \(=325\)
• Y - Int \(=2400\)
• Equation: \(y = 325x+2400\), where \(x\) is the number of months and \(y\) is the amount of savings. The slope \(325\) means \(\$325\) is deposited per month and the \(y -\)intercept \(2400\) is the initial amount in the account when \(x = 0\) (at the time of opening).
• ANSWER \(=\$10200\)