Eyad 3 years ago NOTE:This Is Not A Question,This Is A Tutorial ... *How To Find The Equation of The Line* _____________________________________

I have realized that the Majority of questions are about how to find The Equation of the Line...So here is a Tutorial on finding the equation of the Line through A dialogue and some examples .... Q:*-How do I get the equation of a line ? A:==>That depends on the information you have about the line.If, for example, you know the slope and intercept, then you can simply write down the function without the need for any computation throgh the equation of the line :$\Large y=mx+b$ where m is the slope of the line and b is the y-intercept of the graph of the line. Q:*-What if I'am not given the slope and intercept? A:==>Then Use the most systematic way of obtaining the equation of a line which is "point-slope form" through the equation $\LARGE \frac{y_{2}-y_{1}}{x_{2}-x_{1}}=m$ where m=Slope.. But In Order To Use "Point-slope formula" we should know the following : 1-A point on the line . 2-The slope of the line . *This is all the information we need to know;[Knowing the slope tells us the direction of the line, and knowing a point fixes its position in space]. Here is Some Examples ON getting the slope through the "Point'slope formula" : ___________________________________________________________________________ *_* Example (1):..Find the slope of a line passing through the points: =_=_=_=_= ==>(2 , 3) and (0 , -1) . ==>(-2 , 4)and (-2 , 6) . ==>(5 , 2) and (-7 , 2) . If He gives you two points and need the slope ,Use The "point-slope formula" $\LARGE \frac{y_{2}-y_{1}}{x_{2}-x_{1}}=m$ *_* Example (2):..Find the equation of the line that passes through the point (-2 , 5) and has a slope of -4: =_=_=_=_=_=_= ==>Ans: Substitute y1,x1 and m in the point slope form of a line y - y1 = m(x - x1) y - 5 = - 4(x - (-2)) y = - 4x - 3 . *_* Example(3):Find the equation of the line that passes through the points (0 , -1)and(3 , 5): =_=_=_=_=_=_= ==> Ans: - We first calculate the slope of the line $\Large m=\frac{5 - (-1)}{3 - 0}=\frac{6}{3}=2$ - Use the slope and any of the two points to write the equation of the line using the point slope form. y - y1 = m(x - x1) using the first point y - (-1) = 2(x - 0) y = 2x - 1. *_* Example (4):Find the slope of the line given by the equation -2x + 4y = 6 . ==>Ans: We Need To put the equation as a slope intercept form of a line ==> (y=mx+b) -2x + 4y = 6 -->(add 2x to both sides) 4y = 2x + 6 -->(divide by 4 into both sides) y = (1/2)x + 3/2 -->(Now we have slope intercept form of a line) Therefore,The slope of the line is given by the coefficient of x and is equal to 1/2. __________________________________________________________________________________________ Now Here is two tips: ===================== =-=>Parallel Lines:They are two non vertical lines are parallel ,and [*Their Slope are EquaL ] m1=m2 =-=>Perpendicular Lines:Two non vertical lines are perpendicular if and only if their slopes m1 and m2 are such that m1*m2 = -1 . **Don't Forget These Tips Beacuse they will help you alot in Tricky Questions. ========================================================================================================================== If You Need Any Help ,Please Inform me . Ty

2. lgbasallote

wow incredible! very well written :)

@lgbasallote :Tysm,You 're my role-model is Tutorials :)

4. lalaly

Raheeba ya tasali :P .. great work eyado

5. lgbasallote

why thank you <tips hat>

6. Calcmathlete

Very good :) Only think I suggest is to add a part about when it would be best to use Point-Slope Form and when to use slope-intercept form? Unless I missed it, I don't think there is one.

@lalaly :Shokran ya lanoo ,Haza men ba3d ma 3endakom :)

@Calcmathlete :I mentioned it in the first 2 questions :)

9. Calcmathlete

lol. I did miss it. Nevermind then! :D

Ty ,anyway :)