Graphing Linear Equations in Slope-Intercept Form

Graphs, Functions, and Models

Graphing Linear Equations in Slope-Intercept Form

Linear equations are fundamental in precalculus and are often written in the slope-intercept form:

• Slope-Intercept Form: $y = mx + b$

• Where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).

To graph a linear equation in this form, follow these steps:

1. Identify the y-intercept (b): This is the point (0, b) on the y-axis.

2. Use the slope (m): The slope is the ratio of the rise (vertical change) to the run (horizontal change). From the y-intercept, use the slope to find a second point.

3. Draw the line: Connect the two points with a straight line extending in both directions.

Example

Graph the equation $y = \frac{1}{2}x + 2$:

• y-intercept (b): 2 (plot the point (0, 2))

• Slope (m): $\frac{1}{2}$ (from (0, 2), go up 1 unit and right 2 units to plot a second point)

• Draw a straight line through these points.

Practice Problem

Identify the y-intercept and slope of $y = -\frac{1}{2}x + 1$. Then graph the equation.

• y-intercept (b): 1 (plot the point (0, 1))

• Slope (m): $-\frac{1}{2}$ (from (0, 1), go down 1 unit and right 2 units to plot a second point)

• Draw a straight line through these points.

Key Terms:

• Slope (m): Measures the steepness of the line. Positive slope rises left to right; negative slope falls left to right.

• y-intercept (b): The value of y where the line crosses the y-axis.

Additional info: The slope-intercept form is a foundational concept for understanding more complex functions and graphing techniques in precalculus.