Key Points

✓Linear equations create straight lines when graphed.
✓The slope-intercept form (y = mx + b) is a common way to represent linear equations.
✓The slope (m) indicates the steepness and direction of the line.
✓The y-intercept (b) is the point where the line crosses the y-axis.
✓You only need two points to graph a line.

Linear equations are equations that, when graphed, form a straight line. They can be written in several forms, the most common being slope-intercept form (y = mx + b), where 'm' represents the slope of the line and 'b' represents the y-intercept (where the line crosses the y-axis). To graph a linear equation, you need at least two points. You can find these points by substituting values for 'x' and solving for 'y', or vice versa. Once you have two points, plot them on a coordinate plane and draw a straight line through them. This line represents all the solutions to the linear equation.

Worked Example

Graph the linear equation y = 2x + 1

Step 1: Identify the slope and y-intercept. In this equation, the slope (m) is 2 and the y-intercept (b) is 1.
Step 2: Plot the y-intercept (0, 1) on the coordinate plane.
Step 3: Use the slope to find another point. Since the slope is 2 (or 2/1), move up 2 units and right 1 unit from the y-intercept. This gives you the point (1, 3).
Step 4: Plot the point (1, 3) on the coordinate plane.
Step 5: Draw a straight line through the two points (0, 1) and (1, 3). This line represents the graph of the equation y = 2x + 1.

Answer: The graph is a line passing through (0,1) and (1,3).

Try It Yourself

1. Graph the equation y = x - 2

2. Graph the equation y = -3x + 4

3. Graph the equation 2y = 4x - 6

Watch Out For These Mistakes

Incorrectly identifying the slope and y-intercept from the equation.
Plotting points incorrectly on the coordinate plane.
Drawing the line with the wrong slope (e.g., positive instead of negative).