To graph the equation \( x + 2y = 4 \), we can first rewrite it in slope-intercept form (\( y = mx + b \)).
- Rearranging the equation: \[ 2y = -x + 4 \] \[ y = -\frac{1}{2}x + 2 \]
This shows that the slope (\( m \)) is \( -\frac{1}{2} \) and the y-intercept (\( b \)) is \( 2 \).
-
Plotting the y-intercept: Plot the point \( (0, 2) \) on the graph.
-
Using the slope: From the y-intercept \( (0, 2) \), we can use the slope to find another point. The slope of \( -\frac{1}{2} \) means that for every 2 units you move down (negative direction), you move 1 unit to the right (positive direction).
Starting from \( (0, 2) \):
- Move down 2 units to \( y = 0 \) and then 1 unit to the right to \( x = 1 \). This gives you the point \( (1, 0) \).
-
Plotting another point: You can also find another point by rearranging the original equation. For example, setting \( x = 4 \): \[ 4 + 2y = 4 \implies 2y = 0 \implies y = 0 \] You already have the point \( (4, 0) \).
-
Drawing the line: Once you have at least two points, you can draw a straight line through them.
Here’s a summary of the key points for graphing:
- Points to plot: \( (0, 2) \) and \( (4, 0) \)
- The slope is \( -\frac{1}{2} \).
The line will extend infinitely in both directions. Feel free to use graph paper or a graphing tool to visually represent this linear equation.
1 answer