How to Plot a Graph Using the Equation y mx c

Understanding the Equation y mx c

To plot a graph using the equation y mx c, understanding this fundamental linear equation is essential. Here, the terms are defined as:

y: The dependent variable, representing the output value. x: The independent variable, representing the input value. m: The slope of the line, indicating the rate of change of y with respect to x. c: The y-intercept, where the line crosses the y-axis when x 0.

Step-by-Step Guide to Plotting the Graph

Understand the Equation Identify Values for m and c Choose specific values for m and c. For example, let's say m 2 and c 1. Substitute these values into the equation: y 2x 1. Create a Table of Values x y 2x 1 -2 2(-2) 1 -3 -1 2(-1) 1 -1 0 2(0) 1 1 1 2(1) 1 3 2 2(2) 1 5

This table gives the points: (-2, -3), (-1, -1), (0, 1), (1, 3), (2, 5).

Plot the Points Draw the x-axis horizontally and the y-axis vertically. Mark the points calculated from your table. Draw the Line Connect the points with a straight line. Extend the line across the graph and add arrows on both ends to indicate it continues infinitely. Label the Graph Label the axes appropriately. Optionally write the equation of the line on the graph for clarity.

Example

For the equation y 2x 1:

The line will have a slope of 2, meaning for every 1 unit you move to the right on the x-axis, you move up 2 units on the y-axis. The y-intercept is at (0, 1).

Summary

The process of choosing values for m and c, creating a table of x and y values, plotting the points, drawing the line, and labeling the graph is essential for visualizing the linear relationship represented by the equation y mx c.

The graph of y mx c with m and c as constants is the straight line with slope m and y-intercept c. This line passes through the two points (0, c) and (1, m c).