Answer:
Step-by-step explanation:
You want to find the equation for a line that passes through the two points:
(-2,-5) and (6,3).
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, (-2,-5), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=-2 and y1=-5.
Also, let's call the second point you gave, (6,3), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=6 and y2=3.
Now, just plug the numbers into the formula for m above, like this:
m=
3 - -5
6 - -2
or...
m=
8
8
or...
m=1
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=1x+b
Now, what about b, the y-intercept?
To find b, think about what your (x,y) points mean:
(-2,-5). When x of the line is -2, y of the line must be -5.
(6,3). When x of the line is 6, y of the line must be 3.
Because you said the line passes through each one of these two points, right?
Now, look at our line's equation so far: y=1x+b. b is what we want, the 1 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 (-2,-5) and (6,3).
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:
(-2,-5). y=mx+b or -5=1 × -2+b, or solving for b: b=-5-(1)(-2). b=-3.
(6,3). y=mx+b or 3=1 × 6+b, or solving for b: b=3-(1)(6). b=-3.
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
(-2,-5) and (6,3)
is
y=1x-3
