Arithmetic of Functions problem.
2 answers:
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Answer:
y=+3
Step-by-step explanation:
the equation of a line is y=mx+c
where m is the slope and c 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, (0,3), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=0 and y1=3.
Also, let's call the second point you gave, (-5,3), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-5 and y2=3.
Now, just plug the numbers into the formula for m above, like this:
m=
or
m=
or
m=0
So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+c like this:
y=0x+c
Now, what about c, the y-intercept?
To find c, think about what your (x,y) points mean:
(0,3). When x of the line is 0, y of the line must be 3.
(-5,3). When x of the line is -5, 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=0x+c. c is what we want, the 0 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 (0,3) and (-5,3).
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 c 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:
(0,3). y=mx+c or 3=0x 0+c, or solving for c: c=3-(0)(0). c=3.
(-5,3). y=mx+c or 3=0x -5+c, or solving for c: =3-(0)(-5). c=3.
See! In both cases we got the same value for c. And this completes our problem.
The equation of the line that passes through the points
(0,3) and (-5,3)
is
y=+3
Hope this helps :)