Find an equation for a line passing through (-3, 4) and (2, -6)

The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.

For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:

So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (-3,4), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=-3 and y1=4.

Also, let's call the second point you gave, (2,-6), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=2 and y2=-6.

Now, just plug the numbers into the formula for m above, like this:

m=

-6 - 4

2 - -3

or...

m=

-10

5

or...

m=-2

So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:

y=-2x+b

Now, what about b, the y-intercept?

To find b, think about what your (x,y) points mean:

(-3,4). When x of the line is -3, y of the line must be 4.

(2,-6). When x of the line is 2, y of the line must be -6.

Because you said the line passes through each one of these two points, right?

Now, look at our line's equation so far: y=-2x+b. b is what we want, the -2 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (-3,4) and (2,-6).

So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.

You can use either (x,y) point you want..the answer will be the same:

(-3,4). y=mx+b or 4=-2 × -3+b, or solving for b: b=4-(-2)(-3). b=-2.

(2,-6). y=mx+b or -6=-2 × 2+b, or solving for b: b=-6-(-2)(2). b=-2.

See! In both cases we got the same value for b. And this completes our problem.

The equation of the line that passes through the points

(-3,4) and (2,-6)

is

y=-2x-2