To draw the graph of the equation x + 2y = 4, we need to rearrange the equation to express it in a more familiar form.
Start by solving for y:
1. Rearrange the equation:
2y = 4 – x
2. Divide everything by 2:
y = 2 – (1/2)x
This equation is now in the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
In our case, the slope (m) is -1/2 and the y-intercept (b) is 2. This means that the graph will cross the y-axis at the point (0, 2).
Next, we can find another point by choosing a value for x. For instance, if we let x = 0:
– When x = 0:
y = 2 – (1/2)(0) = 2
So, the first point is (0, 2).
If we let x = 4:
– When x = 4:
y = 2 – (1/2)(4) = 0
So, the second point is (4, 0).
Now we have two points: (0, 2) and (4, 0). Plot these points on a coordinate grid.
Finally, draw a straight line through the two points. This line represents the equation x + 2y = 4.
In summary, plotting the graph involves finding two points on the line, using the slope and y-intercept, and connecting them to represent the linear relationship described by the equation.