Question

Graph by plotting points.
2xequalsminusyplus4

Answer 1

To graph the equation \( 2x = -y + 4 \), we can rearrange it into a more familiar form, such as slope-intercept form ( \( y = mx + b \) ).

Starting with the original equation:

\[
2x = -y + 4
\]

We can add \( y \) to both sides:

\[
2x + y = 4
\]

Then, we can isolate \( y \):

\[
y = -2x + 4
\]

Now we have the equation in slope-intercept form, where:
- The slope \( m \) is \( -2 \)
- The y-intercept \( b \) is \( 4 \)

**Steps to graph the equation:**

1. **Plot the y-intercept (0, 4)**: This is where the line crosses the y-axis.

2. **Use the slope (-2)**: The slope means that for every 1 unit you move to the right along the x-axis, you move down 2 units on the y-axis.

- Starting from (0, 4), if we move 1 unit to the right (to \( x = 1 \)), we move down 2 units to \( y = 2 \) -> point (1, 2).
- From (1, 2), moving 1 unit to the right (to \( x = 2 \)), we would go down 2 units to \( y = 0 \) -> point (2, 0).

3. **Plot these points**:
- (0, 4)
- (1, 2)
- (2, 0)

You can also find additional points by selecting some negative or other x-values.

- If \( x = -1 \):
\[
y = -2(-1) + 4 = 2 + 4 = 6 \rightarrow (-1, 6)
\]

- If \( x = -2 \):
\[
y = -2(-2) + 4 = 4 + 4 = 8 \rightarrow (-2, 8)
\]

Now, plot these points on a graph and draw a straight line through them to represent the equation \( y = -2x + 4 \).

**Graph summary**:
- Points to plot: (0, 4), (1, 2), (2, 0), (-1, 6), (-2, 8).
- Draw a line connecting these points to complete the graph. The line will slope downwards from left to right, indicating a negative slope.