Question

Graph these equations:
x+2y=4
y=
–
1
2
x+2
Click to select points on the graph.

Answer 1

To graph the equations you've provided, we'll start with each equation one at a time.

1. **Equation 1:** \( x + 2y = 4 \)

To convert this into slope-intercept form (\( y = mx + b \)), we can solve for \( y \):
\[
2y = 4 - x
\]
\[
y = -\frac{1}{2}x + 2
\]
So, this is a linear equation with a slope of \(-\frac{1}{2}\) and a y-intercept of \(2\).

2. **Equation 2:** \( y = -\frac{1}{2}x + 2 \)

This equation is already in slope-intercept form and is identical to the rearranged form of the first equation.

### Points for the Graph

Both equations represent the same line. Here are some points you can use to graph this equation:

1. **Y-Intercept**: When \( x = 0 \),
\[
y = -\frac{1}{2}(0) + 2 = 2 \quad \text{(Point: (0, 2))}
\]

2. **Another Point**: When \( x = 2 \),
\[
y = -\frac{1}{2}(2) + 2 = -1 + 2 = 1 \quad \text{(Point: (2, 1))}
\]

3. **Another Point**: When \( x = 4 \),
\[
y = -\frac{1}{2}(4) + 2 = -2 + 2 = 0 \quad \text{(Point: (4, 0))}
\]

4. **Another Point**: When \( x = -2 \),
\[
y = -\frac{1}{2}(-2) + 2 = 1 + 2 = 3 \quad \text{(Point: (-2, 3))}
\]

### Summary of Key Points:
- (0, 2)
- (2, 1)
- (4, 0)
- (-2, 3)

### Drawing the Graph
- Plot the points (0, 2), (2, 1), (4, 0), and (-2, 3) on a coordinate plane.
- Draw a straight line through these points.

Since both equations describe the same line, your graph will represent that single line, and every point satisfy either equation.