LINEAR+EQUATIONS

Slope is the rise over the run. The y-intercept is where the line crosses over the Y axis. **
 * WHAT ARE THE SLOPE AND Y-INTERCEPT?

**In the picture the slope is -4/3 and the y intercept is 3. The slope represents the slant of the line and is negative if the line is slanting to the left (such as in the picture) and positive if it's slanting to the right.In an equation the slope is the coefficiant of the variable, ex. y= 4x+3, 4 is the slope. In an equation the y intercept is the constant, the 3 in the example. [|slope and y intercept practice]** Created by Megan Dister WHAT IS THE DIFFERENCE BETWEEN STANDARD FORM AND SLOPE INTERCEPT FORM?

WHAT IS THE LINE OF BEST FIT? HOW AND WHY DO WE USE IT? GIVEN A SET OF DATA HOW DO WE FIND IT?
 * __The line of best fit is the linear equation that fits into a set of data most accurately.__ We can use it to find the average increase in a set of data. If you have a stat plot with data, you can 1 count the difference and find the slope and y-int from that, or 2 if you have a ti 83+ 84 84+ 84 silver edition you can go to stat, edit, chose a field to edit, and then put the input(x) in on the left and the output(y) on the right.**


 * __input(x)|output(y)|__
 * __1 | 2 |__
 * __2 | 4 |__
 * __3 | 6 |__
 * __4 | 8 |__

__|input(x)|output(y)|__
 * in this stat table, the output is twice the input so the slope is 2 and since nothing needs to be added on the y-int is 0. so the equation would be y=2x+0 or just y=2x. If you where to graph this with a graphing calculator while the stat plot was turned on, this line would hit every point from the stat plot exact.**
 * __1|3|
 * 2|8|
 * 3|5|
 * 4|12|__

[|finding slope and y intercept]  SOLVING SYSTEMS OF EQUATIONS: Substitution Method
 * This chart, however, does not have a definite slope or pattern. As you can see, the one could be 1*2+3, 1+2, 1*3. But the 2 can be 2*4, 2+6, 2*3+2, 2*2+4. The 3 could be 3*2-1 or 3+2 and. So, as you see these do not have the same y-int or slope. Now you must use the line of //__BEST FIT.__ //**First A: if you have a graphing calculator **you can go to stat/edit. Then you inter the x-input in the left column and the y-output data in the right.**

Step 1. sssssss Equation 1. Y=2x+3 Equation 2. X + Y =3 In order to do the substitution method, 1 equation must be in y- intercept form and 1 in X plus Y form. X + (2X+3 )= <span style="color: rgb(0,0,255);">3 Since we know what y equals, we can plug it into problem 2 as shown in Step1. Then we solve to get the equation. 3X+3=3 Step 2. Next we have to solve for X, meaning we have to find what X equals. We need to get X by its self so we subtract 3 from each side. To get X completely by its self, we must divide by 3 to get what X equals. 3X + 3 = 3 - 3 -3

3X = 0

3<span style="color: rgb(255,255,255);">hiopl 3 _<span style="color: rgb(255,255,255);">llllllll

X = 0

Step 3. Equation 1. Y= 2X +3 Equation 2. X + Y= 3 Now that we know what X equals, we go back to the original equations and you can plug what X equals into **any 1 of the two original equations.** This way we can solve for Y also.

Equation 1. Y = 2 (0) + 3 Y= 3 (0,3) This is just a fancy way of saying that X= 0 and Y= 3

Equation 2. X + Y= 3 0 + Y =3 * Note that here that because the equation states 0 + Y, we can conclude that it is just showing Y* Y= 3 (0,3)

<span style="color: rgb(0,0,0);">ELIMINATION METHOD

Equation 1 <span style="color: rgb(255,0,255);">2X + 3Y= 15 Equation 2 <span style="color: rgb(113,191,8);">4X -3Y= 3 In this method to solve X and Y, we use multiplication to get the same coefficient as a corresponding term in a different equation

Step 2.<span style="color: rgb(255,255,255);">ffffffffff 2 ( <span style="color: rgb(0,0,0);"><span style="color: rgb(255,0,255);">2X + 3Y= 15 ) = 4X+6Y=30 =In order to get <span style="color: rgb(255,0,255);">2X like <span style="color: rgb(113,191,8);">4X we need to multiply all of Equation 1 by 2.=

= = <span style="color: rgb(0,0,0);">

=<span style="color: rgb(255,0,0);"> =

Step 3 <span style="color: rgb(255,0,0);">4X + 6Y= 30 <span style="color: rgb(255,255,255);"> kkkkkkk Here, since the 4X's subtract to zero, we are solving for Y. We got 9 Y equals 27. To find Y, we must divide by 9. <span style="color: rgb(255,255,255);">hhhhh - <span style="color: rgb(255,0,0);"> <span style="color: rgb(113,191,8);">4X -3Y= 3 <span style="color: rgb(255,255,255);">kkkkkkk <span style="color: rgb(0,128,0);"><span style="color: rgb(255,255,255);">hhhhhh 9Y= 27 <span style="color: rgb(255,255,255);">kkkkkkkllll uuuuuu 9<span style="color: rgb(255,255,255);">lllllll 9 <span style="color: rgb(255,255,255);">pppppp Y = 3

Step 4<span style="color: rgb(255,255,255);">kkkk Equation 1. 4X- 3(3)=3<span style="color: rgb(255,255,255);"> Now that we know what Y equals we can plug it back **any 1 of the two original equations.**<span style="color: rgb(0,0,0);"> Then we can solve for x <span style="color: rgb(255,255,255);">kkkkkkkkkkkkkkkkkkkkkk 4X-9=3 <span style="color: rgb(0,0,0);"><span style="color: rgb(255,255,255);">kkkkkkkkkkkkkkkkkkkkkk 4X=12 <span style="color: rgb(255,255,255);">kkkkkkkkkkkkkkkkkkkkkk  X= 3 <span style="color: rgb(0,0,0);"> Equation 2.<span style="color: rgb(255,255,255);">llllllllllllllllll 2X + 3(3)= 15 <span style="color: rgb(255,255,255);">kkkkkkkkkkkkkkkkkkkk 2X + 9= 15 <span style="color: rgb(255,255,255);">kkkkkkkkkkkkkkkkkkk 2X= 6 <span style="color: rgb(255,255,255);">kkkkkkkkkkkkkkkkkkk X=3 <span style="color: rgb(255,255,255);">kkkkkkkkkkkkkkkkkkk (<span style="color: rgb(0,0,0);"> ( 3,3) <span style="color: rgb(0,0,0);"> Substitution and Elimination Methods created by Thomas Boswick __<span style="color: rgb(0,114,255); font-family: 'Comic Sans MS',cursive;">[|**Useful Links** http://www.tpub.com/math1/13d.htm] []__ <span style="color: rgb(0,114,255); font-family: 'Comic Sans MS',cursive;">

SOLVING SYSTEMS OF EQUATIONS: Matrix Method **Step 1: Turn on Graphing Calculator Step 2: Push __2nd__ & __x-1__ to get to the matrix page Step 3: Scroll over to __Edit__ and click on the first matrix (or whatever matrix you want to edit) Step 4: Take the equation you are trying to solve (ex: 4x + 2y= 16 and x + y= 6) and make the size of the matrix 2x3 Step 5: In the upper left hand corner, fill in the space with the coefficient of the x in the first equation <span style="color: rgb(255,0,0);"> __ 4 __x + 2y= 16. In the upper middle of the matrix, fill in the space with the coefficient of the y in the first equation 4x + <span style="color: rgb(255,0,0);"> __ 2 __y= 16. In the upper right hand corner, fill in the space with the answer of the equation 4x + 2y=__<span style="color: rgb(255,0,0);">16 __ ** = Step 6: Repeat Step 5, but instead of usind the first equation, use the second equation (x + y=6) =

= Step 7: Push __2nd__ __mode__ = = Step 8: Push __2nd__ __x-1__ = = Step 9: Scroll over to __Math__   = = = = Step 10: Scroll down to where it says __rref(__ and click = = = = = = Step 11: Push __2nd__ __x-1__ = = Step 12: Scroll down to the letter of the Matrix you chose to edit and click on it = = Step 13: Push the button with the symbol ) on it and push enter = = Step 14: Look at the two numbers in the top right hand corner, and in the bottom right hand corner. The one in the top right hand corner is what x equals, and the one in the bottom right hand corner is what y equals. = = = = = = = = = = http://www.infj.ulst.ac.uk/NI-Maths/Ks4/CaseStudies/tx_ti_82/Matrices/Matrices.htm = = = =   = = = = = = = = = = = = = = = = = = = = = = ALL BY: SAVANNAH KITTERMA N = = = = = = = = = = = = = = = = = = =