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?

(1 point)
Responses

3y=−2x+24
3 y equals negative 2 x plus 24

2x+3y=24
2 x plus 3 y equals 24

y−6=−23(x−3)
y minus 6 equals negative Start Fraction 2 over 3 End Fraction left parenthesis x minus 3 right parenthesis

y=−23x+8

Answer 1

To find the equation of the line that passes through the points given in the table, we start by determining the slope (m) and then use the point-slope form of the equation.

The points given are:
- (0, 8)
- (3, 6)
- (6, 4)
- (9, 2)
- (12, 0)

Let’s calculate the slope (m) using two points, for example (0, 8) and (3, 6):

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - 8}{3 - 0} = \frac{-2}{3}
\]

Now that we have the slope \( m = -\frac{2}{3} \), we can use the point-slope form of the equation of a line:

\[
y - y_1 = m(x - x_1)
\]

Using the point (3, 6):

\[
y - 6 = -\frac{2}{3}(x - 3)
\]

To write this in standard form, we can manipulate the equation to fit \( Ax + By = C \):

1. Distribute \(-\frac{2}{3}\):
\[
y - 6 = -\frac{2}{3}x + 2
\]

2. Add 6 to both sides:
\[
y = -\frac{2}{3}x + 8
\]

3. To convert to standard form, multiply through by 3 to eliminate the fraction:
\[
3y = -2x + 24
\]

Rearranging gives us:
\[
2x + 3y = 24
\]

Thus, the correct standard form of the equation is:

**2x + 3y = 24**

So, the correct response from the options given is:

**2x + 3y = 24**