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Graph the equation 2x - y = 4 using the form y = mx + b.

A. (1, 2), (0, -4)
B. (1, -1), (0, -3)
C. (-2, -2), (0, 1)
D. (1, -2), (0, -4)

1 answer

To graph the equation \( 2x - y = 4 \) using the form \( y = mx + b \), we need to rearrange the equation into that form.

Starting with the equation: \[ 2x - y = 4 \]

We can isolate \( y \) by adding \( y \) to both sides and subtracting 4 from both sides: \[ -y = -2x + 4 \]

Now, multiply both sides by -1 to solve for \( y \): \[ y = 2x - 4 \]

Now, we have the equation in slope-intercept form \( y = mx + b \), where the slope \( m = 2 \) and the \( y \)-intercept \( b = -4 \).

Finding Points

We can find two points on the line by substituting different values for \( x \):

  1. When \( x = 0 \): \[ y = 2(0) - 4 = -4 \] Point: \( (0, -4) \)

  2. When \( x = 1 \): \[ y = 2(1) - 4 = 2 - 4 = -2 \] Point: \( (1, -2) \)

So the two points we have found are \( (0, -4) \) and \( (1, -2) \).

Choose the Correct Option

The correct answer corresponds to the points we found:

  • \( (1, -2) \)
  • \( (0, -4) \)

This matches option: D. (1, -2), (0, -4).