Algebra Period 4

Find the Equation of a Line
: 7-6

1) We know how to GRAPH a line by 3 points where we decide what to plug in and chug

Usually, we just try 0, 1, 2 first


2) We know how to GRAPH a line by intercepts...we plug in zero for y and x and chug

This works really well when the line is in STANDARD form and the coefficients are factors
 of the constant on the other side of the equation.


3) We know how to GRAPH a line by using slope-intercept form:


We isolate y on one side

We read the y intercept (the b which is the constant on the other side)

We graph that value on the y axis

We COUNT to the next point by reading the slope, the coefficient of the x


The slope should be read as the y value (+up or -down)
and then the x value (+ right or - left)


If the slope is not a fraction, make it a fraction by putting the integer over 1



TODAY WE'RE NOT LEARNING TO GRAPH ANOTHER WAY...WE'RE LEARNING HOW TO FIND THE EQUATION OF A LINE

We usually use the slope-intercept form of the line as our "template"

We know that y = mx + b so


we can substitute in what we know (what the problem gives us)
 and solve for whatever we're missing!


[The problem will give you enough information to know the slope or know the y intercept! Then you'll solve for the missing item.]



It helps to memorize this little rhyme


Oh mystery line,
What could you be?

If I could just find you,

y = mx + b


If I could find m

And I could find b.

Then I could put it together

And I would see:

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 or counting it if you have the graph


2) Do I have the y intercept (b)? If not, find it by plugging in a point and the slope and solving for b or if you have the graph, just read it on the y axis.


3) Don't forget to put it all together in one equation at the end!



THERE ARE 5 CASES THAT YOUR BOOK INCLUDES:


First case:
You're given the slope and the y intercept
 (easiest case) 
m = 3/2 and 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 the slope and need to find the intercept (b)


(3, 1) is a point on the line and 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 the y intercept and need to find the slope


(3, 1) is still a point on the line, but this time you know 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) are 2 points on the line


You need to first find the slope using the formula:

m = change in y / change in x = 3 - (-3)/ 1 - (-2) = 6/3 = 2


Now plug the slope in with one (you pick the easiest!) 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