You want to find the equation for a line that passes through the two points:
(-7,-10) and (-5,-20).
First of all, remember what the equation of a line is:
y = mx+b
here, m is the slope, 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.
Consider (-7,-10) as point #1, so the x and y numbers given will be called x1 and y1. Or, x1=-7 and y1=-10.
Consider (-5,-20), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-5 and y2=-20.
Now, just plug the numbers into the formula for m above, like this:
m= (-20 - -10)/(-5 - -7)
m= -10/2
m=-5
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=-5x+b
Now, what about b, the y-intercept?
To find b, think about what your (x,y) points mean:
(-7,-10). When x of the line is -7, y of the line must be -10.
(-5,-20). When x of the line is -5, y of the line must be -20.
Because line passes through each one of these two points, right?
Now, look at our line's equation so far: y=-5x+b. b is what we want, the -5 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 specifically passes through the two points (-7,-10) and (-5,-20).
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:
(-7,-10). y=mx+b or -10=-5 × -7+b, or solving for b: b=-10-(-5)(-7). b=-45.
(-5,-20). y=mx+b or -20=-5 × -5+b, or solving for b: b=-20-(-5)(-5). b=-45.
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 (-7,-10) and (-5,-20) is y=-5x-45.
