d=√ (y2-y1)2 + (x2-x1)2d=√ (y2-y1)2 + (x2-x1)2

Distance FormulaDistance Formula

d=√ (yd=√ (y22-y-y11))22 + (x + (x22-x-x11))22

For example, consider the two points A (2,5) and B (5,1),For example, consider the two points A (2,5) and B (5,1), so:  x1 = 2,  y1 = 5,  x2 = 5, and y2 = 1.so:  x1 = 2,  y1 = 5,  x2 = 5, and y2 = 1. Substituting into the distance formula we have:Substituting into the distance formula we have: d= √(1-5)d= √(1-5)2 2 +(5-2)+(5-2)2 2

d= √(4)d= √(4)2 2 +(3)+(3)22

d =√16+9d =√16+9

d =√25d =√25 d =5d =5

ALWAYS REMEMBER THE FORMULA OF DISTANCE THEN SUBSTITUTE THE

GIVEN POINTS!!!

EXAMPLE:

FIND THE MIDPOINT BETWEEN (7,3) AND (5,2)

USING THE MIDPOINT FORMULA SUBSTITUTE THE GIVEN POINTS IF X1=7,Y1=3 AND X2=5,Y2=2

LETS TRY ANOTHER QUESTIONS:LETS TRY ANOTHER QUESTIONS: THE LINE SEGMENT FROM B (1,-3)TO C(H,K)HAS ITS MIDPOINT THE LINE SEGMENT FROM B (1,-3)TO C(H,K)HAS ITS MIDPOINT

AT (4,5)FIND THE AT (4,5)FIND THE H H AND AND KK . . SO YOU NOTICED THAT THE MIDMOINT IS GIVEN ..DONT SO YOU NOTICED THAT THE MIDMOINT IS GIVEN ..DONT

WORRY JUST FOLLOW THE FORMULA OF MIDPOINT;WORRY JUST FOLLOW THE FORMULA OF MIDPOINT; FIRST,IDENTIFY THE NUMBER AS SHOWN BELOWFIRST,IDENTIFY THE NUMBER AS SHOWN BELOW B(XB(X11=1 and Y=1 and Y1 1 = -3) MP(X= -3) MP(XMM=4 and Y=4 and YM M =5) C(X=5) C(X2 2 = = H H and Yand Y22= = KK))

USED THE USED THE

INFORMATIONINFORMATION

ABOVE THEN ABOVE THEN

SUBSTITUTE IT TO SUBSTITUTE IT TO

THE GIVEN FORMULATHE GIVEN FORMULA

STEP 2 : IN ORDER TO ELIMINATE THE 2 JUST SIMPLY MULTIPLY IT ON THE STEP 2 : IN ORDER TO ELIMINATE THE 2 JUST SIMPLY MULTIPLY IT ON THE BOTH SIDESBOTH SIDES

8=1+H 8=1+H STEP 3 : STEP 3 : Transpose 1 to the left sideTranspose 1 to the left side

8-1=H 8-1=H STEP 4:STEP 4: YOU SHOULD ALWAYS CHANGE THE SIGN EVERYTIME YOUR YOU SHOULD ALWAYS CHANGE THE SIGN EVERYTIME YOUR

TRANPOSING A CERTAIN NUMBER.TRANPOSING A CERTAIN NUMBER.

Here is an example of how to do slope formula:-The slope m passes through the points of (2, 4) and (3, 5)-Label the points: x1 y1 x2 y2 ( 2 , 4 ) (3 , 5) Using slope formula: y2 – y1 5-4 1 x2 – x1 3-2 1

That means that the slope m is 1

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The Table of values system shows what you could get for Y, if The Table of values system shows what you could get for Y, if X is a certain number. For example:X is a certain number. For example:

Y = X – 9 Y = X – 9 Lets say we Lets say we wanted X to bewanted X to be -1.-1.

Y= X – 9Y= X – 9 Y= (-1) – 9Y= (-1) – 9

Y=-10Y=-10 * You can put any number for X. * You can put any number for X.

X

YX

-1 -10

0 -9

1 -8

There are different equations you can use to receive your answer:There are different equations you can use to receive your answer:1)1) Ax+By+C=0 Ax+By+C=0 Standard form. Standard form.2)2) Y=mx+bY=mx+b Slope Y-intercept form. Slope Y-intercept form.3)3) Y-y1=m(x-x1) Point-slope formY-y1=m(x-x1) Point-slope form4)4) Ax+By=CAx+By=C

The X-intercept happens when the y-intercept equals to zero. For example:The X-intercept happens when the y-intercept equals to zero. For example:3x+8y+24=03x+8y+24=03x+8(0)+24=0 3x+8(0)+24=0 *The zero takes the place of the Y or X *The zero takes the place of the Y or X3x+24=03x+24=0 3 33 3X= 8X= 8

The Y-intercept happens when the X- intercept equals to zero. For example:The Y-intercept happens when the X- intercept equals to zero. For example:5x+2y+18=05x+2y+18=05(0)+2y+18=05(0)+2y+18=02y + 18=02y + 18=0 2 22 2Y=9Y=9

For Slope Y-intercept we use the equation: For Slope Y-intercept we use the equation: Y=mx+bY=mx+b

If your equation is Y=1/3x+4If your equation is Y=1/3x+4

Then you will put this on a graph by labeling it as Then you will put this on a graph by labeling it as 1/3 would be your 1/3 would be your rise over runrise over run. Your Y (4) will . Your Y (4) will be put over one. So, it will become:be put over one. So, it will become:

M=1 Y=4 Now, you are going to graph M=1 Y=4 Now, you are going to graph 3 1 these points.3 1 these points.

slopey-intercept

First, you are First, you are going to rise going to rise 4,now that you 4,now that you have that point have that point from there you from there you are going to are going to rise one and rise one and run three.run three.

This is you rising 4.

This is you rising 1.

And this is you running 3.