How do you graph y = 2x - 2?

To graph the equation y = 2x - 2, follow these steps:

Identify Key Components

This equation is in slope-intercept form, y = mx + b, where:

• m is the slope (2 in this case)
• b is the y-intercept (-2 here)

Plot the Y-Intercept

Start by plotting the y-intercept. This is the point where the line crosses the y-axis:

• For b = -2, place a point at (0, -2).

Use the Slope

The slope of 2 means that for every 1 unit you move to the right (positive x-direction), you move up 2 units (positive y-direction). From the y-intercept:

• Move right 1 unit to (1, -2).
• Then move up 2 units to (1, 0).

Draw the Line

After plotting at least two points, draw a straight line through them. This line represents the equation y = 2x - 2.

Check Your Work

To ensure accuracy, you can pick another x-value, substitute it into the equation, and see if the corresponding y-value lies on your line. For example:

• If x = 2, then y = 2(2) - 2 = 2. Plot the point (2, 2) to confirm.

Now you have a complete graph of the equation!