(-3,-3) and (5,2). First of all, remember what the equation of a line is:
y = mx+b Where: m is the slope, and b is the y-intercept First, let's find what m is, the slope 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, (-3,-3), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=-3 and y1=-3. Also, let's call the second point you gave, (5,2), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=5 and y2=2.
Now, just plug the numbers into the formula for m above, like this:
m= 2 - -3 5 - -3 or...
m= 5 8 or...
m=5/8 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=5/8x+b Now, what about b, the y-intercept? To find b, think about what your (x,y) points mean: (-3,-3). When x of the line is -3, y of the line must be -3. (5,2). When x of the line is 5, y of the line must be 2. Because you said the line passes through each one of these two points, right? Now, look at our line's equation so far: y=5/8x+b. b is what we want, the 5/8 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,-3) and (5,2).
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,-3). y=mx+b or -3=5/8 × -3+b, or solving for b: b=-3-(5/8)(-3). b=-9/8. (5,2). y=mx+b or 2=5/8 × 5+b, or solving for b: b=2-(5/8)(5). b=-9/8. 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,-3) and (5,2)
