To graph the equation y = 2x + 6, you’ll want to start by identifying the key components of the line.
First, recognize that this equation is in the slope-intercept form, which is y = mx + b. Here, ‘m’ represents the slope and ‘b’ represents the y-intercept. In our case, the slope (m) is 2, and the y-intercept (b) is 6.
Next, begin at the y-intercept, which is the point (0, 6). This is where the line crosses the y-axis. From there, use the slope to find another point. The slope of 2 means that for every 1 unit you move to the right (in the positive x direction), you move up 2 units (in the positive y direction).
Starting from (0, 6), move right to (1, 6) and then up 2 units to (1, 8). Another point on the line is (1, 8).
For more accuracy, you can find additional points by continuing to apply the slope. For example, from (1, 8), move right 1 unit to (2, 8) and up 2 units to (2, 10). This gives you another point: (2, 10).
After plotting these points on a graph, draw a straight line through them, extending the line in both directions. This line represents all the solutions to the equation y = 2x + 6.
In summary, by identifying the y-intercept and using the slope to plot additional points, you can successfully graph the equation y = 2x + 6.