To graph the equation 2y = x + 4, we need to convert it into the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
1. **Rearranging the Equation**:
Start by isolating y in the equation:
2y = x + 4
Divide both sides by 2 to get:
y = (1/2)x + 2
2. **Identify the Slope and Y-intercept**:
From the equation y = (1/2)x + 2, we can identify:
– The slope m = 1/2, which means for every 2 units you move to the right along the x-axis, you move 1 unit up along the y-axis.
– The y-intercept b = 2, indicating the graph will cross the y-axis at the point (0, 2).
3. **Plotting Points**:
To graph this line accurately, you can plot a few points. Start with the y-intercept (0, 2):
– When x = 0, y = 2 → point (0, 2)
– When x = 2, y = (1/2)(2) + 2 = 3 → point (2, 3)
– When x = -2, y = (1/2)(-2) + 2 = 1 → point (-2, 1)
4. **Drawing the Graph**:
On a Cartesian plane, plot the points you found: (0, 2), (2, 3), and (-2, 1).
Then, draw a straight line through these points extending in both directions. This line represents the equation 2y = x + 4.
5. **Final Considerations**:
Remember that the line is infinite in both directions; thus, you can also find additional points if you want more precision.
By following these steps, you’ll have a clear graph for the equation, illustrating the relationship between x and y.