Graph: y = x - 6
To graph the equation y = x - 6, we will create a coordinate plane with an x-axis and a y-axis. Then we will plot points to represent different values of x and y that satisfy the equation.
To graph a linear equation in the form y = mx + b, where m is the slope and b is the y-intercept, we can use the slope-intercept method.
In our equation, y = x - 6, the coefficient of x is 1, which represents the slope of the line. Additionally, the y-intercept is -6, which represents the point where the line crosses the y-axis.
To begin, plot the y-intercept, which is the point (0, -6). This point indicates that when x = 0, y = -6.
Next, find another point on the line. You can choose any value for x to determine the corresponding value for y. Let's choose x = 2. By substituting x = 2 into the equation, we get y = 2 - 6 = -4. So another point on the line is (2, -4).
To plot more points, you can repeat this process by choosing different values for x and finding the corresponding values for y. Alternatively, you can use the slope. In this case, since the coefficient of x is 1, the slope is 1 (rise of 1 over a run of 1).
Starting from the point (0, -6), you can move up 1 unit and right 1 unit to get to the next point. Then repeat this process to plot more points.
After plotting multiple points, connect them with a straight line. This line represents the graph of the equation y = x - 6.
Note that this line will continue infinitely in both directions since there are no restrictions mentioned in the equation.