Ask a New Question
Menu

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

1 answer

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