Graphing Linear Equations and Finding the Equation of a Line

Graphs, Functions, and Models

Finding the Equation of a Line

In Precalculus, understanding how to find the equation of a line given certain information is a foundational skill. This topic involves using points and slopes to write equations and graph lines on the coordinate plane.

• Point-Slope Form: The equation of a line with slope m passing through point $(x_1, y_1)$ is given by: $y - y_1 = m(x - x_1)$

• Slope-Intercept Form: The equation of a line with slope m and y-intercept b is: $y = mx + b$

• Graphing a Line: To graph a line, plot the given point and use the slope to find a second point. Draw a straight line through both points.

Example

• Given: A line passes through the point (3, 5) with a slope of 2.

• Equation: Using point-slope form: $y - 5 = 2(x - 3)$

• Convert to Slope-Intercept Form: $y - 5 = 2x - 6$ $y = 2x - 1$

• Graph: Plot the point (3, 5) and use the slope (rise 2, run 1) to plot a second point. Draw the line through these points.

Additional info: The worksheet image shows a coordinate grid for graphing and a partially written equation, indicating a typical Precalculus exercise on linear equations.