Ask a New Question
Menu

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=−2x+3y=−3x−2

{y=2x−2y=3x+3

{y=2x+3y=3x−2

{y=3x+2y=−2x+3
Skip to navigation

1 answer

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

Analyzing \( y_a \)

  1. From the table:
    • When \( x = 0 \), \( y_a = 3 \)
    • When \( x = 1 \), \( y_a = 5 \)
    • When \( x = 2 \), \( y_a = 7 \)

The change in \( y_a \) as \( x \) increases by 1 is:

  • From 3 to 5 (an increase of 2)
  • From 5 to 7 (an increase of 2)

This indicates the slope \( m_a = 2 \).

Using the point-slope form \( y - y_1 = m(x - x_1) \): Using the point \( (0, 3) \): \[ y_a - 3 = 2(x - 0) \] \[ y_a = 2x + 3 \]

So, the equation for \( y_a \) is: \[ y_a = 2x + 3 \]

Analyzing \( y_b \)

  1. From the table:
    • When \( x = 0 \), \( y_b = -2 \)
    • When \( x = 1 \), \( y_b = 1 \)
    • When \( x = 2 \), \( y_b = 4 \)

The change in \( y_b \) as \( x \) increases by 1 is:

  • From -2 to 1 (an increase of 3)
  • From 1 to 4 (an increase of 3)

This indicates the slope \( m_b = 3 \).

Using the point-slope form \( y - y_1 = m(x - x_1) \): Using the point \( (0, -2) \): \[ y_b + 2 = 3(x - 0) \] \[ y_b = 3x - 2 \]

So, the equation for \( y_b \) is: \[ y_b = 3x - 2 \]

Conclusion

In conclusion, the system of linear equations is:

  1. \( y_a = 2x + 3 \)
  2. \( y_b = 3x - 2 \)

Among the options given, the correct answer is: {y=2x+3 y=3x−2}