This tutorial covers graphing a line using slope intercept form, through the definition and discussion of:
- Graphs and Equations: A Review
- Slope Intercept Form Equations
- Graphing Slope Intercept Form Equations
1. Graphs and Equations: A Review
It’s often useful to graph equations in order to visually represent the relationship between variables. To graph a line, you only need to find at least two points on the line. There are several ways to graph a line:
- Pick two values for x and find their corresponding y values to plot the points.
- Write an equation in a certain form to easily identify important information about the line.
2. Slope Intercept Form Equations
The slope intercept form of an equation can be used to more easily graph a line. Equations in slope intercept form look like this:
This formula is called "slope intercept form" because you can easily identify the slope and the y-intercept of the line. In this equation, the variable m represents the slope of the line.
Recall that the slope of a line is its steepness. You find the slope by dividing the change in y-coordinates by the change in x-coordinates, so you can also think of slope as rise over run.
The variable b in the equation represents the y-intercept of the line. The coordinate point of the y-intercept is (0, b) and the y-intercept is the location on a graph where a line or a curve intersects the y-axis.
3. Graphing Slope Intercept Form Equations
You can visually identify slope and a y-intercept on a graph. Consider the equation of this graph:
You can see that the y-intercept is -1, which corresponds to the -1 value of b in your equation.
The slope of the line can be found by finding the rise over the run. Starting from the y-intercept, locate the next easily identifiable point on the line. From the y-intercept, you can see that you rise 2 and have a run of 3 in the positive direction. Therefore, the slope is 2 over 3, which corresponds to the m value in your equation.
You can use the variables in an equation in slope intercept form to actually graph the equation. Suppose you have the equation:
Step 1: Start by identifying the y-intercept, which is the b value. In your equation, then, the y-intercept is 2, which is at the coordinate point (0, 2) on the graph.
Step 2: Looking back at your equation, you want to look for the slope, which is the m value. The slope is 1/5, so the rise is 1 and the run is 5. Starting from a y-intercept, this means that you go up 1 and over 5 in the positive direction to find a second point.
Step 3: Finally, you can connect the points to create a line representing the equation.
Now that you know how to graph an equation in slope intercept form, try graphing the equation:
- Start by identifying the y-intercept, which, again, is the b value. Therefore, the y-intercept is 6 and at the coordinate point (0, 6) on the graph.
- Next, referring back to your equation, look for the slope, which is the m value. The slope is -3, which you can write as a fraction, -3/1, meaning that the rise is -3 and the run is 1. Starting at your y-intercept, this means that you go down 3 and over 1 in the positive direction to find a second point.
- Finally, connect the points to create a line representing the equation.
Today you reviewed graphs and equations, noting that to graph a line, you only need to find at least two points on the line. You also learned about the slope intercept form, called this because in equations that have this form, you can easily identify the slope and the y-intercept from the equation. Lastly, you learned how to graph slope intercept form equations, using the easily identifiable variables representing slope and the y-intercept.