a line passes through (-8,3) and (-6,4).What is the equation of the line?

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, (-8,3), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=-8 and y1=3.

Also, let's call the second point you gave, (-6,4), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-6 and y2=4.

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

m=

4 - 3

-6 - -8

or...

m=

1

2

or...

m=1/2

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=1/2x+b

Now, what about b, the y-intercept?

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

(-8,3). When x of the line is -8, y of the line must be 3.

(-6,4). When x of the line is -6, y of the line must be 4.

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

Now, look at our line's equation so far: y=1/2x+b. b is what we want, the 1/2 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 (-8,3) and (-6,4).

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:

(-8,3). y=mx+b or 3=1/2 × -8+b, or solving for b: b=3-(1/2)(-8). b=7.

(-6,4). y=mx+b or 4=1/2 × -6+b, or solving for b: b=4-(1/2)(-6). b=7.

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