How to Create a Graph of the Linear Equation y = 2x + 6?

To graph the linear equation y = 2x + 6, we need to follow a few simple steps:

1. Identify the slope and y-intercept: In the equation y = 2x + 6, the coefficient of x (which is 2) represents the slope of the line. This means that for every unit increase in x, y increases by 2. The constant term (6) represents the y-intercept, the point where the line crosses the y-axis. So, we know the line will cross the y-axis at (0, 6).
2. Plot the y-intercept: Start by plotting the y-intercept (0, 6) on the graph. This is our first point.
3. Use the slope to find another point: Starting from the y-intercept (0, 6), use the slope to find another point. Since the slope is 2, you can go up 2 units and 1 unit to the right from (0, 6) to get to the point (1, 8).
4. Plot the second point: Plot the point (1, 8) on the graph.
5. Draw the line: Finally, connect the points with a straight line, extending it in both directions. Make sure to add arrows at the ends of the line to indicate that it continues infinitely.

This will give you a graph that corresponds to the linear equation y = 2x + 6. It’s a straight line that rises steeply because of the slope of 2, indicating that y increases at a relatively fast rate as x increases.