Graphing Equations in Slope Intercept Form
Learning Objective(s)
· Give the slope intercept form of a linear equation and define its parts.
· Graph a line using the slope intercept formula and derive the equation of a line from its graph.
Introduction
Straight lines are produced by linear functions. That means that a straight line can be described by an equation that takes the form of the linear equation formula, 
. In the formula, y is a dependent variable, x is an independent variable, m is a constant rate of change, and b is an adjustment that moves the function away from the origin. In a more general straight line equation, x and y are coordinates, m is the slope, and b is the [y-intercept]. Because this equation describes a line in terms of its slope and its y-intercept, this equation is called the slope-intercept form.
The graph below represents any line that can be written in slope intercept form. It has two slider bars that can be manipulated. The bar labeled m lets you adjust the slope, or steepness, of the line. The bar labeled b changes the y-intercept. Try sliding each bar back and forth, and see how that affects the line.
That was fun, eh? You should have noticed that changing the value of m could swivel the line from horizontal to nearly vertical and through every slope in between. As m, the slope, gets larger, the line gets steeper. When m gets smaller, the slope flattens.
Changing the value of b moved the line around the coordinate plane. A positive y-intercept means the line crosses the y-axis above the origin, while a negative y-intercept means that the line crosses below the origin.
Simply by changing the values of m and b, we can define any straight line. That’s how powerful and versatile the slope intercept formula is.
How is the x-intercept represented in the slope intercept form of a linear equation?
A) It is represented by x.
B) It is represented by m.
C) It is represented by b.
D) It is not represented.
Now that we understand the slope intercept form, we can look at the graph of a line and write its equation just from identifying the slope and the y-intercept. Let’s try it with this line:
The slope intercept form is . For this line, the slope is 
, and the y-intercept is 4. If we put those values into the formula, we get the equation 
. That’s the slope intercept equation of our line.
and the y-intercept is -3. The correct answer is
From Equation to Graph
We’ve seen that it’s not difficult to convert the graph of a line to an equation. We can also work the other way and produce a graph from a slope intercept equation. Consider the equation 
. This equation tells us that the y-intercept is at -1. We’ll start by plotting that point, (0, -1), on a graph.
The equation also tells us that the slope of this line is -3. So we’ll count up 3 units and over -1 unit and plot a second point. (We could also have gone down 3 and over +1.) Then we draw a line through both points, and there it is, the graph of 
.
?
B) 
D) 
Summary
The slope intercept form of a linear equation is written as , where m is the slope and b is the value of y at the y-intercept. Because we only need to know the slope and the y-intercept to write this formula, it is fairly easy to derive the equation of a line from a graph and to draw the graph of a line from an equation.
