Use the table to answer the question.%0D%0A%0D%0Ax- and y-Values%0D%0Ax%090%093%096%099%0912%0D%0Ay%098%096%094%092%09%0D%0A0%0D%0A%0D%0AWrite the standard form of the equation of the line going through the points in the table. Which of the following options is correct?%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0Ay−6=−23(x−3)%0D%0Ay minus 6 equals negative Start Fraction 2 over 3 End Fraction left parenthesis x minus 3 right parenthesis%0D%0A%0D%0A3y=−2x+24%0D%0A3 y equals negative 2 x plus 24%0D%0A%0D%0Ay=−23x+8%0D%0Ay equals negative Start Fraction 2 over 3 End Fraction x plus 8%0D%0A%0D%0A2x+3y=24%0D%0A2 x plus 3 y equals 24

Answer 1

To find the equation of the line that passes through the points provided in the table, we will first calculate the slope (m) of the line using the formula:

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

Let's use the points (3, 6) and (6, 4):

• \( (x_1, y_1) = (3, 6) \)
• \( (x_2, y_2) = (6, 4) \)

Now we can calculate the slope:

\[ m = \frac{4 - 6}{6 - 3} = \frac{-2}{3} \]

Now that we have the slope, we can use point-slope form of the line equation, which is:

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

Using the point (3, 6):

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

To convert this into standard form \(Ax + By = C\), we will start with the point-slope form obtained:

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

First, multiply each term by 3 to eliminate the fraction:

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

Expanding both sides gives:

\[ 3y - 18 = -2x + 6 \]

Now, rearranging to standard form \(Ax + By = C\):

\[ 2x + 3y = 24 \]

Thus, the standard form of the equation of the line going through the points in the table is:

\[ 2x + 3y = 24 \]

Now, looking at your provided options, the correct choice is:

2x + 3y = 24.