Don bought a car after 12 months he had paid $5 140. After 36 months he paid $13,420. Create a linear equation to represent the amount of money he has paid as a function of months

Answer 1

To create a linear equation representing the amount of money Don has paid as a function of months, we need to determine the slope and y-intercept of the line using the information provided.

Let \( x \) be the number of months and \( y \) be the total amount paid.

We have the following two data points:

1. After 12 months: \( (12, 5140) \)
2. After 36 months: \( (36, 13420) \)

First, we calculate the slope (m) of the line using the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Where:

• \( (x_1, y_1) = (12, 5140) \)
• \( (x_2, y_2) = (36, 13420) \)

Now substituting the values:

\[ m = \frac{13420 - 5140}{36 - 12} = \frac{8280}{24} = 345 \]

Next, we can use the slope and one of the points to write the equation in point-slope form \( y - y_1 = m(x - x_1) \).

Let's use the point \( (12, 5140) \):

\[ y - 5140 = 345(x - 12) \]

Now, let's simplify the equation:

\[ y - 5140 = 345x - 4140 \]

Adding 5140 to both sides, we get:

\[ y = 345x + 1000 \]

Thus, the linear equation representing the amount of money Don has paid as a function of months is:

\[ y = 345x + 1000 \]

Answer 2

Options
y -5,140=345(x-36)
y-36,=345(x-13420)
y-13,420=345(x-36)
y+5140=345(x-12)

Answer 3

Based on the options provided, we can identify the correct choice.

From our previous solution, we derived the linear equation representing the amount Don has paid as a function of months:

\[ y = 345x + 1000 \]

This means that the corresponding point-slope form of the equation would relate to the data points we have.

Since one of the points is \( (36, 13420) \), we can express it in point-slope form:

We have:

• \( y - 13420 = 345(x - 36) \)

However, this does not appear in any of the options directly.

Instead of using that point, let's examine the options:

1. Option: \( y - 5,140 = 345(x - 36) \)

   • This is a correct point-slope form using the point \( (5,140, 12) \) and the slope we calculated. But it uses \( x = 36 \) incorrectly.

2. Option: \( y - 36 = 345(x - 13420) \)

   • This is not a sensible equation based on the points we have.

3. Option: \( y - 13,420 = 345(x - 36) \)

   • Similar to option 1, for point (36, 13420), but with \( x = 36 \) incorrectly.

4. Option: \( y + 5,140 = 345(x - 12) \)

   • This is the correct point-slope form derived from the initial point \( (12, 5140) \).

Since our derived equation is similar to the form in option 4, that is the likely answer, phrased incorrectly as it suggests addition instead of subtraction.

To summarize, from the options you provided, option 4: \[ y + 5140 = 345(x - 12) \] is the correct choice if interpreted with the understanding that this follows the structure but is written in a slightly odd form.

Thus, the best option is indeed:

y + 5140 = 345(x - 12) (though it should instead state that the starting point for y is 5140 with a downward adjustment).