What is the Slope Intercept Form?
The slope intercept form is a formula that identifies the slope and the y intercept of a straight line.
From our post entitled “What is Slope?”, you will remember that the slope measures how steep the line is.
The y intercept is the place where the line crosses the y axis.
You can also think of the y intercept as the value of y when x equals zero.
Slope Intercept Formula
The formula is as follows:
Slope intercept form
y = mx + b
In the slope-intercept formula, these variables are used:
y = the y coordinate
m = slope
x = the x coordinate
b = the y intercept
Example of the Slope Intercept Form
Now have a look at the following example.
y = 3x + 4
The slope of the line is 3 and the y intercept is 4.
The y intercept tells us that the point (0,4) lies on this line.
Putting Other Equations into the Slope Intercept Form
An equation of a single line can take various forms.
As you know, you can solve linear equations by substituting values in the equation.
In addition, you can get to the slope-intercept form by changing the standard equation of a line.
For instance, consider the equation of a line:
–2x + 5y = 10
We can get the above equation into the slope-intercept form in three steps.
First, isolate the y term to the left:
–2x + 5y = 10
5y = 10 + 2x
Then divide by 5 to solve for y:
5y = 10 + 2x
5y ÷ 5 = (10 + 2x) ÷ 5
y = 2 + 2x/5
Finally, reorganize the right side of the equation to get the slope-intercept form.
y = 2 + 2x/5
y = 2x/5 + 2
Graphing with Slope-Intercept
Let’s look at the previous equation again.
y = 2x/5 + 2
We can use this equation in order to graph the line.
First, plot the y intercept, which is point (0,2).
Then use the slope to count the spaces to the next point.
The slope in our example is 2/5.
Remember that the change in the y coordinate is given in the top of the fraction for the slope formula.
The change in the x coordinate is given in the bottom of the fraction
In other words, the top number in the fraction shows how many units we need to move to up.
The bottom number in the fraction shows how many units we need to go to the right.
So, the next point is five units to the right and two units higher than the present point.
