Find the equation of a line through the points?

Question

(-2, 3) and (3,8)

Here is another one I have like this that I cant figure out.

(4,6) and (6,2)

Answer 1

To find the line between any two points, you need the slope and the y-intercepts. The line has the equation Y = mX + b, where m is the slope and b is the Y-intercept.

Point are given as (X, Y) pairs. Since you have two sets, let's call them (X1, Y1) and (X2, Y2).

The slope, m, is (Y2-Y1)/(X2-X2), or the rise divided by the run. Take one set of your points, (X1, Y1) and plug these values into the equation:

Y1 = mX1 + b and solve for b.

Answer 2

The first thing you have to do is find the slope of the line which passes through the two points.

The equation to find slope m is m = (ycoordinate2 - ycoordinate1) / (xcoordinate2-xcoordinate1). Then, for (-2, 3) and (3,8), m = (8-3)/(3-(-2))= 5/5 = 1. So the slope of the line is 1.

The next thing you would do is plug the found slope and one set of points into the equation of a line to find the y-intercept.

The equation of a line is y = mx + b, where m is the slope and b is the y-intercept and (x,y) is any point on the line. Then, y = 1x + b. Now, plug in any one of the ordered pairs given, either (-2, 3) or (3,8). I picked (3,8). Then, 8 = 1*3 + b. Now, solve for b. 8 = 1*3 + b = 3+b, so b = 5.

The last thing you have to do is put all the pieces of information into the equation of a line y = mx + b. You know that m = 1 and b = 5 so the equation fo the line is y = 1x + 5.

You are done! Hope this helped

Answer 3

y = mx + b is your friend:
For the first equation:
3 = -2m + b
8 = 3m + b
subtracting the second from the first yields:
5 = 5m so m=1
plugging into 1 yields
3 = -2 + b ==> b = 5
so y = x + 5 is the equation.
For the second
6 = 4m + b
2 = 6m + b
Subtracting the two equations yields
-4 = 2m ==> m = -2
plug into the first
6 = -8 + b ==> 14 = b
so y = -2x + 14 is the answer you seek.

Answer 4

Here's a concept you should remember.

Imagine a line through (-2,3), taking any point (x,y) on the line, get the slope of this line

slope1 = (y-3) / (x-(-2))

Imagine a line through (3,8), taking any point (x,y) on the line, get the slope of this line

slope2 = (y-8) / (x-3)

Now, if the line is going through (-2,3) and (3,8), doesn't that mean slope1 = slope2?

i.e.

(y-3) / (x-(-2)) = (y-8) / (x-3)

solve it

(x+2)(y-8) = (x-3)(y-3)
xy - 8x + 2y - 16 = xy - 3x - 3y + 9
y = x + 5

The second one, please try it yourself.

Answer 5

slope = 8-3/(3--2)= 5/5 = 1

(y-3)/(x--2) = 1
y-3=x+2
y=x+5


Do the same for the next one...
(2-6)/(6-4)=-4/2=-2
(y-6)/(x-4)=-2
y-6 = -2(x-4) = -2x + 8
y = -2x +14

Answer 6

dude, y=mx+b. Just find the slope first, that is m, then plug in the other point. Capish?

Answer 7

-find slope
-after that it depends of which specific equation you intend to put the information in!

Answer 8

y2-y1=m(x2-x1)....

y2= 8
y1= 3

x2= 3
x1= -2

solve for m

then put it in here...
y= mx +b

or something like that- look in your book for the right formulas and do it yourself so you can pass your damn math test. that is the point of math homework.

Answer 9

the first one is
y=x+5

the second one is
y= -2x+14

Answer 10

why dont you use the equation you were given. all you need to do is plug in it into y=mx+b