Question

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)

Answer 1

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)**.