Question

Use the table to answer the question.
x- and y-Values
x 0 3 6 9 12
y 8 6 4 2 0
Write the standard form of the equation of the line going through the points in the table. Which
of the following options is correct?

Answer 1

To find the standard form of the equation of the line that passes through the given points, we will first identify two points from the provided data. The table lists the following points:

- (0, 8)
- (3, 6)
- (6, 4)
- (9, 2)
- (12, 0)

We can choose any two points, but let's use (0, 8) and (12, 0) for calculation.

1. **Calculate the slope (m)** of the line using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using points (0, 8) and (12, 0):
\[
m = \frac{0 - 8}{12 - 0} = \frac{-8}{12} = -\frac{2}{3}
\]

2. **Use the point-slope form of the equation of the line**, which is:
\[
y - y_1 = m(x - x_1)
\]
Using the point (0, 8):
\[
y - 8 = -\frac{2}{3}(x - 0)
\]
Simplifying this:
\[
y - 8 = -\frac{2}{3}x
\]
\[
y = -\frac{2}{3}x + 8
\]

3. **Convert to standard form (Ax + By = C)**:
To put it in the form Ax + By = C, let's rearrange the equation:
\[
\frac{2}{3}x + y = 8
\]

To eliminate the fraction, multiply the entire equation by 3:
\[
2x + 3y = 24
\]

Therefore, the standard form of the equation of the line that goes through the given points is:
\[
2x + 3y = 24
\]

You should check which of the options you have correlates to this equation.