How do I find the equation of a line using two points of a line?

Question

I've been having a LOT of trouble with this lately. The coordinate points (A & B) are (0,-3) and (3,3). You may have to graph this on a plot.

How bout I'll put a sample question for you to solve because I'm not really getting some of the answers. How bout when the coordinates are (4,7) and (2,9).

Answer 1

(0,-3) and (3,3)
m = (3 - (-3))/(3 - 0)
m = (3 + 3)/3
m = 6/3
m = 2

(0,-3), m = 2
-3 = 2(0) + b
-3 = 0 + b
b = -3

ANS : y = 2x - 3

for a graph, go to http://www.calculator.com/calcs/GCalc.html

only type in 2x - 3, then click enter on the keyboard.

---------------------------

(4,7) and (2,9).

m = (9 - 7)/(2 - 4)
m = (2)/(-2)
m = -1

(4,7), m = -1
7 = -1(4) + b
7 = -4 + b
b = 11

ANS : y = -x + 11

Answer 2

To solve this problem you need two equations:
y=mx+b and m= (x1-x2)/(y1-y2). It doesn't matter which set of points you make (x1,y1) and which one you make (x2,y2). the important thing is that you subtract the x and y from the same set from the x and y in the other set.
So for this problem let (x1,y1) = (0,-3) and let (x2,y2) = (3,3). By plugging these numbers into the slope equation (m= (x1-x2)/(y1-y2)) we get m=(0-3)/(-3-3). This can be simplified to (-3)/(-6) which can again be simplified to give you 1/2. Now you know that m= 1/2 you can take this information and one of your points and plug them into the equation y=mx+b. It doesn't matter which points you use as long as your x and y come from the same set. We'll use the points (0,-3) here, so by pugging in we get: -3=(1/2)(0)+b. This works out to a nice easy algebra problem which can be solved as follows:
-3=(1/2)(0)+b
-3=0+b
b=-3
Now you know m=1/2 and b= -3 you can put these numbers into your general line equation y=mx+b to get
y=(1/2)x-3
and you're done.

Answer 3

The equation for a line has two "unknowns", the slope and the intercept.
The slope is easy to find if you have the coordinates of the two points; it is just the "rise over the run". Or in your case, slope = (3 - (-3))/(3 - 0) = 2 . . . The difference in the y values (rise) divided by the difference in the x values (run).

You can get the intercept by plugging in the values for one of the points into the equation for a line.
y = n x + b
-3 = 2 * 0 + b
b = -3

Your equation is:
y = 2 x -3

Answer 4

First effective the slope employing the slope formulation y2-y1 -------- x2-x1 -5 - 0 -------- -2 - 8 = -5 ----- -10 simplified equals a million/2 then plug that into factor slope equation y-y1 = m(x-x1) (%. the two factor to replace into x1 and y1 y-0 = a million/2(x-8) y= a million/2x - 4 performed

Answer 5

first find your slope.
y1 minus y2 over x1 minus x2
y1= -3
y2= 3
y1-y2= -3-3= -6

x1=0
x2=3
x1-x2= 0-3= -3
now take -6 divided by -3 which equal 2. that gives you your slope
now use the equation y=mx+b
m is your slope which you now is 2 so plug that in. now take one on your points that you were given and substitute for y and x. (this way you can solve for b which is your y-intersept) so now you have.... -3=2(0)+b...now solve for b
2 times 0 is 0 so you are left with -3=b.
now go back to your equation...y=mx+b....y=2x-3

Answer 6

Use the two points to find the slope of the line (Y1-Y2)/(X1-X2). Then use one of the points to make point-slope form. Then you have a graph-able equation.

Answer 7

not much word, see this:
(y-y1)=(y2-y1)/(x2-x1)*(x-x1)
(use this equation for solve linear eq. with two coordinate known)
then enter the coordinate, it does not matter who is the "1" or the "2":
(y-(-3))=(3-(-3))/(3-0)*(x-0)
y+3=2x, or:
y=2x-3.

Answer 8

y = mx+b, where m = slope. to find slope, do (y2-y1)/(x2-x1). after you get "m", then use one of the points... either (0,-3) or (3,3) and plug into "y" and "x" to get b. then rewrite the equation as y=(slope found)x+(b found) =)

Answer 9

if u were using the slope intercept formula y =mx+b(i think) where m = slope and b = y intercept
u would use the y intercept plus the slope which u can find by using (y2-y1/x2-x1)

Answer 10

slope= (-3-3)/(0-3)
= -6/-3=2

y-(-3)=2(x-0)
y=2x-3