Introduction to Linear Equations
You already know how to plot ordered pairs. Now let us look at graphing linear equations.
In the graph shown, we want to find the equation of the graphed line. To accomplish this we introduce linear equations. You have unknowingly been working with linear equations, so this is NOT a new concept for you.
Most likely you have been working with the standard form of a line, which is Ax + By = C. This is a linear equation with two unknown variables, x and y.
The standard form of the line in the graph is 2x + y = 5, where A =2, B = 1, and C = 5.
We want to rearrange this equation and put it into the y-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. In this form, it is very simple to graph.
Just solve the standard equation for “y” and you have the y- intercept form.
Note: This form will be your BEST FRIEND!! You will continue to see it throughout your algebra studies.
We begin by finding the y-intercept form of the line in the above graph:
What is the y-intercept form of this line: 2x + y = 5 ?Hint: Reread the comment beside the light bulb.
y = 2x + 5 y = 2/5x y = -2x + 5
When this light bulb icon appears throughout this lesson, the information that follows is extremely helpful to you.