equation of a line.. help please?

Question

i have a tset coming every 2 days of so and this one is about equation of a line.. can someone explain to me how to do it with the formulas and show an example.. thanks!

i need to know how to work them with these formulas :

y - y1 = m(x - x1)

Ax + By + C = 0

Answer 1

The first one you use when you have a point and the slope. So, given a point P(x1, y1) on the line, and a slope of m, then you do a straight plug in into the first formula.

The second one you can use if you have two points, but it's actually easier if you find the slope of the line first, and then use the first formula. Then you can put it in the format of the second formula by putting everything on one side.

For example, suppose you have a point (2, 1) and a slope of 2. Using the first method, you would have:

y - 1 = 2(x - 2)
y = 2x - 3

Then just put everything on one side:
2x - y - 3 = 0

Answer 2

Okay, the first formula, y-y1=m(x-x1) is the point-slope formula. Use this one when you are given a point on a line and a slope. (You can also find it if you have the slope of a perpendicular line- the slope is the negative reciprocal, which means switch the sign and flip the fraction.)

Say you have a point, (3,1) and a slope of 2/3.

Plug in the numbers:
y-1=(2/3)(x-3)

Next, solve for y by adding 1 to both sides.
y=(2/3)(x-3)+1

Distribute m (2/3) throughout the parenthesis.
y=(2/3)x-(2/3times3)+1

y=(2/3)x-2+1
y=(2/3)x-1

That's going from point-slope to slope-intercept (y=mx+b) form, which is usually the formula you graph from.

The other equation is Standard form.
Ax+By+C=0
I can't think how this is used, except to go into another form, either point-slope or slope intercept. It can't be used to graph, but you may be asked to find another equation with it. Hopefully, you know how to solve for y. I'm not really sure what kind of questions you'll need this for (I had algebra1 2 years ago, sorry).

Answer 3

The first formula is called point-slope form.
The second formula is called standard form.

Often the form y=mx+b, also called slope-intercept form, is the most useful, but point-slope and standard forms have their uses.

The advantage to point-slope form is that you don't need the y-intercept. Consider the question: Find the equation of a line with slope 3 that includes the point (2,5). You can plug that right into point-slope form to get (y-5) = 3(x-2).

The A, B, and C in standard form don't usually come right out of the question. You have to solve for standard form using an equation you already have. So in our example above, we could do the following:
(y-5)=3(x-2)
y-5 = 3x - 6
-3x + y = -1
-3x + y + 1 = 0
3x - y - 1 = 0

And now we have standard form, with A = 3, B = -1, C = -1. Most textbooks require that A be positive, so that's why I multiplied by -1 in the last step.

Now suppose you have an equation y = 2x - 3 and you want that in point-slope form. We need a point. But we already have a point: y = 2x - 3 tells us that the y-intercept is -3, so (0, -3) is a point on the line. We can also see that the slope is 2, so in point-slope form we would have (y-(-3))=2(x-0), which reduces to (y+3)=2x. If we wanted to take it further into standard form, we could do -2x + y + 3 = 0, so 2x - y - 3 = 0.

Удачи! (If that doesn't look like cyrillic, you need to install the font).

Answer 4

Example
Find equation of line with gradient 2 that passes thro` (3 , 5)
Applying your formula:-
x1 = 3 , y1 = 5 , m = 2
y - 5 = 2 (x - 3)
y - 5 = 2x - 6
y = 2x - 6 + 5
y = 2x - 1
This may be re arranged to give:
2x - y - 1 = 0
This is in form AX + By + C = 0 where:-
A = 2 , B = - 1 , C = - 1

Answer 5

i know how to do the 1st one: you are gonna be given two set of points, lets say (5,7) and (8, 9) then u find the slope using this formula: y2-y1/x2-x1 so you use the points given y2 is 9
y1 is 7, 9-7=2
x2 is 8
x1 is 5, 8-5=3
so the slope is 2/3 which is m is the equation. then u replace y1 and x1 with one set of numbers.the 2 possible answers are:
y-7=2/3(x-5) or y-9=2/3(x-8)

Answer 6

http://en.wikipedia.org/wiki/Linear_equation

sorry that I'm unable to explain it myself (I suck at this stuff). Good luck!