Algebra Period 3

Finding the Equation of a Line 7-6

Always remember that y = mx + b and you can substitute and solve for whatever you're missing!
It helps to memorize this little rhyme:
Oh mystery line,
What can you be?
If I could only find you,
y = mx + b

So first I find m
Then I find b.
Now put it all together
And you've found me!
y = mx + b

The rhyme has 3 steps and usually you will have 3 steps or questions to ask yourself:
1) Do I have the slope (m)? If not, find it by using the slope formula
2) Do I have the y intercept (b)? If not, find it by plugging in a point and the slope
3) Don't forget to put it all together in one equation at the end.

HERE ARE THE 5 CASES THAT THE BOOK INCLUDES:

First case:You're given the slope and the y intercept (easiest case)
m = 3/2 b = -7/5
Just plug in to the generic slope intercept equation: y = 3/2 x - 7/5

Second case: You're given a point and and the slope and need to find the intercept (b)
(3, 1) m = 2
Plug in the point and the slope and solve for b
1 = 2(3) + b
1 = 6 + b
b = -5
Now put it altogether with the given slope and the intercept you just found:
y = 2x -5

Third case: You're given a point and and the y intercept and need to find the slope
(3, 1) b = 2
Plug in the point and the y intercept and solve for slope
1 = 3m + 2
-1 = 3m
m = -1/3
Now put it altogether with the given intercept and the slope you just found:
y = -1/3 x + 2

Fourth case: You're given 2 points and need to find the slope and the intercept
(1 , 3) and (-2 , -3)
You need to first find the slope:
m = change in y / change in x = 3 - (-3)/ 1 - (-2) = 6/3 = 2
Now plug the slope in with one of the points and find the intercept b
3 = 2(1) + b
3 = 2 + b
b = 1
Finally, put it all together:
y = 2x + 1

Fifth case: You have a graph of a line and need to determine the equation
Look at the graph and find 2 easy points to use to find the slope (make sure they are integers!)
(If the y intercept is not an integer, then follow fourth case completely)
Put the information together in y = mx + b form


Another way to find the equation with 1 point and slope-
Point Slope Form of the equation

You know one point and the slope. This is the same case a the SECOND CASE, but there is a ANOTHER WAY to solve it other using slope intercept form. This is not the most common way. Most people use the slope intercept form for all cases.

This one is very specific, but many students love it! (It is MY personal favorite!!)

Point-slope form of a line: You know one point and the slope. Use the following formula:
y - y₁ = m (x - x₁)

Using the same example from the second case above: (3 , 1) and m = 2
y - 1 = 2 (x - 3)
Simplify: y - 1 = 2x - 6
y = 2x - 5

If you're trying to link the slope intercept form to the point slope form of the same line:

The point slope version eliminates one step from using the slope intercept form. In the slope intercept form, you plug in the point and slope, solve for b, and then rewrite the equation using the intercept that you found. In point slope form, once you plug in the point and slope, you just simplify and the equation is already done!