y - y
= m(x - x)
( x
, y
) = coordinates of any point on the line
Goal: To write the equation of a line knowing 2 pieces of information about that line.
It is simple to write the equation for any line from a graph or by using some given information. You'll need to use the POINT-SLOPE form of a line:
|
y - y |
m = slope ( x |
If you are given this information, just substitute it into the equation
Example 1: m = -4 and (3, 2) is on the line
y - y
= m(x - x)
y - 2 = -4(x - 3)
|
y - 2 = -4x + 12 |
Simplify to "y = " form |
y = -4x + 14
First calculate the slope, then proceed as above.
Example 2: ( -2, 1) and (3, 4) are on the same line
Recall the slope formula m = (y
- y
) / (x
- x)
In our example, m = (4 - 1) / (3 - -2) = 3/5 or m = (1 - 4) / (-2 - 3) = 3/5 Same result!!
Now finish like example 1. You may use either point in the formula.
| y - y
= m(x - x
) |
y - y
= m(x - x
) |
| y - 1 = (3/5)(x - -2) | y - 4 = (3/5)(x - 3) |
| y - 1 = (3/5)x + 6/5 | y - 4 = (3/5)x - 9/5 |
| y = (3/5)x + 11/5 | y = (3/5)x + 11/5 |
| SAME RESULT! | |
If you only have a graph, choose any 2 points on the graph of the line to work with. Picking the x-intercept and y-intercept as your points makes the calculation simple. Once you have chosen the points, follow the steps in Example 2
 |
(0, 2) |
| (-3, 0) |
Try these problems to perfect your skill in writing the equations of lines. Check by graphing your equations on your calculator to see if the points are on your lines.
1. slope = 2/3 point (6, 7)
2. slope = 4 point (3, 0)
3. points (4, 11) and (5, 9)
4. points (-9, 9) and (0, 1)
5. 