Linear Functions

There are three different ways to write linear functions. They are slope-intercept, point-slope, and standard form. There are certain situations where it is better to use one way than another to solve a problem. It is important to understand and comprehend the mechanics of these three forms so that you know what form to use when solving a problem.

The first form, point-slope, is written as y-y1=m(x-x1). M is the slope and x1 and y1 correspond to a point on the line. It's good to use this form when you know the slope of a line and one point on it. In order to solve a problem and write an equation using the point-slope form you need two things. Those things are a point on the line, (x,y), and the slope of the line. For example, say the slope of your line is 4 and a point on the line is (1,5).

You would insert the 4 in place of the m, the 1 in place of the x1, and the 5 in place of the y1. When you plug everything into the point-slope equation you get: y-5=4(x-1).

The second form, slope-intercept, is written as y=mx+b. M is the slope and b is the y-intercept. It is good to use this form when you know the slope of a line and the

y-intercept. For example, say that you are given a y-intercept of 6 and a slope of 3. You would insert the 6 in place of the b and the 3 in place of the m. When you plug in your values into the slope-intercept equation you get: y=3x+6.

The last form, standard form, is written as ax+by=c. The letters a, b, and c are integers. X stands for the x-intercept and y stands for the y-intercept.