Question

Table of Values

x
ya yb
0 3 18
1 6 1312
2 9 9
Which of the following systems of linear equations does the table of values represent?

(1 point)
Responses

{y=−3x+3y=412x+18

{y=3x+3y=−412x+18

{y=3x+3y=412x+18

{y=3x+3y=412x−18

Answer 1

To determine which system of linear equations the table of values represents, we need to analyze the points provided in the table and find equations that fit them.

The table of values is as follows:

\[
\begin{array}{c|c|c}
x & y_a & y_b \\
\hline
0 & 3 & 18 \\
1 & 6 & 1312 \\
2 & 9 & 9 \\
\end{array}
\]

### Finding the equation for \( y_a \)

Using the three points:

1. \((0, 3)\)
2. \((1, 6)\)
3. \((2, 9)\)

We can find the slope (m) using the formula:

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

Using points (0, 3) and (1, 6):

\[
m = \frac{6 - 3}{1 - 0} = 3
\]

Now, using the point-slope form \(y - y_1 = m(x - x_1)\), we can determine the equation for \(y_a\):

Using point (0, 3):

\[
y - 3 = 3(x - 0) \implies y = 3x + 3
\]

### Finding the equation for \( y_b \)

Now, let's analyze the points for \( y_b \):

1. \((0, 18)\)
2. \((1, 1312)\)
3. \((2, 9)\)

Finding the slope between points (0, 18) and (1, 1312):

\[
m = \frac{1312 - 18}{1 - 0} = 1294
\]

Using point (0, 18):

\[
y - 18 = 1294(x - 0) \implies y = 1294x + 18
\]

Since we only need the equations that represent \(y_a\) as derived above, we conclude:

\[
y_a = 3x + 3
\]

This matches with the options in the question. The equation for \(y_a\) is part of all the response options presented.

Comparing with the options provided:

1. \(y = -3x + 3, y = 4, 12x + 18\)
2. \(y = 3x + 3, y = -4, 12x + 18\)
3. \(y = 3x + 3, y = 4, 12x + 18\)
4. \(y = 3x + 3, y = 4, 12x - 18\)

The correct choice based on identified \(y_a\) is:

\[
\{y = 3x + 3, y = 4, 12x + 18\}
\]

Thus, the answer is:

**{y = 3x + 3, y = 4, 12x + 18}**.