Linear Functions
Slope-Intercept Form
Point-Slope Form
You’ll need to know the formula for the equation of a line like the back of your hand (actually, better than the back of your hand, because who really knows what the back of their hand looks like anyway?). You have two options about how to write the equation of a line. Both of them require that you know at least two of the following pieces of information about the line:
1. A point, 2. Another point, 3. The slope, m, or 4. The y-intercept, b
If you know any two of these things, you can plug them into either formula to find the equation of the line.
Slope-Intercept Form
The equation of a line can be written in slope-intercept form as
where m is the slope of the function and b is the y-intercept, or the point at which the graph crosses the y-axis and where x=0. The slope, represented by m, is calculated using two points on the line, (x1,y1) and (x2,y2), and the equation you use to calculate m is
To find the slope, subtract the y-coordinate in the first point from the y-coordinate in the second point in the numerator, then subtract the x-coordinate in the first point from the x-coordinate in the second point in the denominator.
Point-Slope Form
The equation of a line can also be written in point-slope form as
In this form (x,y) is one point on the line, and (x1,y1) is the other. Just as with slope-intercept form, m is still the slope of the function. To use this form, find m the same way you did in slope-intercept form, then simply plug in your two points to the point-slope formula.
