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Algebra Slope

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by

Charles Crews

on 4 November 2013

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Transcript of Algebra Slope

The equation for standard form
is Ax+By=C. y=x-3
first step move the x then it will be
-x+y=-3
but you are not done yet the x is negative so you flip the signs it will be.
x-y=3
the slope intercept form
the equation is y=mx=b
ex: y=2x-3y
Rise over run?
First you must graph the points. Then you form a triangle from the two points write down how much it rises put that on top of the fraction, and count how many blocks it runs and put it on the bottom of the fraction!
Finding Slope Using Two Points!
For this example we will use the points (-2,5) and (3,-4).
Using the Equations!
Slope-intercept Form
y = mx + b
Objective
Students will understand the concept of slope!
Vocab!
Slope- rate of change
X- intercept- where the line crosses the X axis
Y- intercept- where the line crosses the Y axis
Coefficient- The number that comes before a variable.
Constant- A term that never changes.
Algebra Slope
This is the formula used to find it!
Y1 - Y2
X1 - X2
X1 Y1
X2 Y2
y coordinate
Examples
The slope
So let's replace the variables with the coordinating numbers and solve!
5 + 4
-2 - 3
x coordinate
=
9
-5
y-intercept
This is our slope!
Writing an equation with two points!
Remember how we found slope with two points? Let's use that example to then create an equation in slope-intercept form using those two points: (-2,5) and (3,-4).
First, take one of the points and the slope of 9/-5 that we found earlier. Let's use the point (-2,5).
Next take the formula y=mx+b and replace them with the corresponding numbers. Using y as 5, x as -2, and m as 9/-5
5 =
9

-5
* - 2 + b
Now Solve For 'b'!
5 = 18/5 +b
25/5 = 18/5 + b
-18/5
-18/5
7/5 = b
Now Write it In Slope-Intercept Form!
y =
9
-5
+
X
7
5
Examples

Slope- intercept form

y = 2x + 3 y = 1/4 + 7
Standard Form
4x + 2y = 3 2x - 5y = 6
Lets use these points to find the slope!

(5,4), (9,1)

First to find the slope you have to put the change in y over the change in x!

y1 - y2 soo.. 4 - 1
x1 - x2
5 - 9
Your slope would be...
3
-4
Finding 'm'
To find 'b' enter in one set of the coordinates in the example and the slope so the equation will look like this...

5 = (3/-4) (4) + b

The first step is to multiply everything by negative four to get rid of the fraction.

-20 = (3) (-16) + b

Then multiply three and negative sixteen to get negative forty- eight

-20 = -48 + b

Add forty- eight to both sides and 'b' will equal twenty- eight!

28 = b
Graphing
Lets do some graphing! For this we will use the point of (-6 , -1) and slope of 2/3. First lets get the equation in slope intercept form by finding 'b'
-1 =
2
3
* -6 + b
- 1 =
-12
3
+ b
-1 = -4 + b
b = 3
y =
2
3
x + 3
Lets graph it! Lets start at the y intercept of (0, 3) and draw a line to the point (-6,-1)!
Let's also use standard form! Ax + By = C
good job!
Finding 'b'
y=
2
3
x + 3
2
3 x + y = 3
-
*-3
2x -
3y = -9
Now lets use a T chart to find the intercepts by replacing variables.
x y
0 ?
? 0
Replace x with 0 and then divide both sides by -3
-3y = -9
y = 3
Replace y with 0 and divide both sides by 2
2x = -9
-9
2
x = -4
1
2
And now you can plot The Points you get and draw a line using the table!
x y
0 3
-4.5 0
(0,3) (-4.5,0)
Full transcript