Example: Write down the equation of the line which passes through the two points (-2, 4) and (3, -5).

Solution

At first glance it might not appear which we'll be capable to use the point-slope form of the line since this need a single point (we've got two) & the slope (that we don't have). However, this fact that we've got two points isn't actually a problem; actually, we can employ these two points to find out the missing slope of the line since we do know that we can always determine that from any two points on the line.

Thus, let's begin my finding the slope of the line.

                                  m = -5 - 4 / 3 - ( -2)  = - 9 /5

Now, which point have to we employ to write down the equation of the line? Actually we can use either point. To illustrate this we will use both.

First, we'll use ( -2, 4) .  Now that we've gotten the point all that we have to do is plug into the formula. We will employ the second form.

                              y = 4 - 9/5 ( x - ( -2)= ( 4 - 9/5 (x + 2)

Now, let's use (3, -5).

y = -5 - 9/5 (x - 3)

Okay, we claimed that it wouldn't matter that point we utilized in the formula, however these sure look like distinct equations.  However it turns out that these actually are the same equation. To illustrate this all that we have to do is distribute the slope through the parenthesis and then simplify.

Following is the first equation.

y = 4 - 9 /5( x + 2)

= 4 - 9/5 x - 18/5

= - (9/5) x + 2/5

Following is the second equation.

y = -5 - 9/5 ( x - 3)

= -5 - 9/5 x + 27/5

= - 9 /5x + 2/5

Thus, sure enough they are the same equation.