To graph the equation 6x + 3y = 18, we first need to rearrange it into the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
1. Start by isolating y in the equation:
3y = 18 – 6x
2. Divide every term by 3 to solve for y:
y = -2x + 6
Now we have the equation in slope-intercept form. From this, we can see that the slope (m) is -2 and the y-intercept (b) is 6. This means that the line crosses the y-axis at the point (0, 6).
3. Next, we can plot the y-intercept (0, 6) on a graph.
4. To find another point, we can use the slope. The slope of -2 means that for every 1 unit you move to the right (positive x-direction), you move down 2 units (negative y-direction). Starting from (0, 6), if we move 1 unit to the right to x = 1, we move down 2 units to y = 4, giving us the point (1, 4).
5. Plot the second point (1, 4).
6. Finally, draw a straight line through the points (0, 6) and (1, 4). This line represents the graph of the equation 6x + 3y = 18.
The graph will extend infinitely in both directions while maintaining the same slope. This line shows all the possible solutions to the equation.