Question

Use the table to answer the question.

Table of Values

x
ya
yb

0 3 −2

1 5 1
2 7 4
Which system of linear equations is represented by the table of values?

(1 point)
Responses

{y=3x+2y=−2x+3

{y=−2x+3y=−3x−2

{y=2x+3y=3x−2

{y=2x−2y=3x+3

Answer 1

To determine the system of linear equations represented by the given table of values, we need to identify the equations for \( y_a \) and \( y_b \) based on the \( x \) values provided.

**For \( y_a \):**

Using the points (0, 3), (1, 5), and (2, 7), we can determine the slope \( m \) and the y-intercept \( b \).

1. Calculate the slope \( m \):
- From (0, 3) to (1, 5):
\[
m = \frac{5 - 3}{1 - 0} = \frac{2}{1} = 2
\]

- From (1, 5) to (2, 7):
\[
m = \frac{7 - 5}{2 - 1} = \frac{2}{1} = 2
\]

Since the slope is consistent, we can use the point-slope form:
\[
y - y_1 = m(x - x_1)
\]

Using point (0, 3):
\[
y - 3 = 2(x - 0) \implies y = 2x + 3
\]

**For \( y_b \):**

Using the points (0, -2), (1, 1), and (2, 4), we will also determine the slope \( m \) and y-intercept \( b \).

1. Calculate the slope \( m \):
- From (0, -2) to (1, 1):
\[
m = \frac{1 - (-2)}{1 - 0} = \frac{3}{1} = 3
\]

- From (1, 1) to (2, 4):
\[
m = \frac{4 - 1}{2 - 1} = \frac{3}{1} = 3
\]

2. Using the point-slope form again:
Using point (0, -2):
\[
y - (-2) = 3(x - 0) \implies y = 3x - 2
\]

**Thus, the two equations derived from the table are:**
1. \( y = 2x + 3 \) (for \( y_a \))
2. \( y = 3x - 2 \) (for \( y_b \))

Now, let's match this with the response options provided:

- {y=3x+2 y=-2x+3}
- {y=-2x+3 y=-3x-2}
- {y=2x+3 y=3x-2}
- {y=2x-2 y=3x+3}

The correct system of equations that matches our results is:

**{y=2x+3 y=3x-2}**.