Calculating Slope and Graphing Linear Equations

This page provides practical examples of calculating slope and graphing linear equations using the slope-intercept form.

Example: To calculate the slope between points (3, 4) and (7, 1): m = (y₂ - y₁) / (x₂ - x₁) = (1 - 4) / (7 - 3) = -3 / 4

This example demonstrates how to apply the slope formula to find the rate of change between two points on a line.

The guide then outlines steps for graphing a linear equation in slope-intercept form:

1. Plot the y-intercept
2. Use the slope to find additional points
3. Continue this process to plot more points and draw a straight line

Example: To graph y = -2x + 5:

1. Plot the y-intercept at (0, 5)
2. Use the slope of -2 to go down 2 units and right 1 unit from the y-intercept to find the point (1, 3)
3. Continue this process to complete the graph

This method provides a systematic approach to graphing linear equations, helping students visualize the relationship between slope, y-intercept, and the resulting line on a coordinate plane.

Intercepts and Slopes

This page introduces the concept of intercepts in linear equations and provides methods for finding them.

Definition: x-intercepts are the points on the graph that cross the x-axis (y = 0), while y-intercepts are the points on the graph that cross the y-axis (x = 0).

To find x-intercepts, set y = 0 in the equation and solve for x. The resulting point will be in the form (x, 0). For y-intercepts, set x = 0 and solve for y, resulting in a point of the form (0, y).

Example: For the equation 2x - 3y = 6, the x-intercept is found by setting y = 0: 2x - 3(0) = 6 2x = 6 x = 3 Therefore, the x-intercept is (3, 0).

Similarly, the y-intercept is found by setting x = 0: 2(0) - 3y = 6 -3y = 6 y = -2 Thus, the y-intercept is (0, -2).

This method provides a systematic approach to finding intercepts, which is crucial for graphing linear equations and understanding their behavior.