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=[tex]\frac{3-3}{-5-0}[/tex]
or
m=[tex]\frac{0}{-5}[/tex]
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 :)
y = 3
First find the gradient of the line:
(Y²-Y¹)/(X²-X¹)
(3-3)/(-5-0)
0/-5 = 0
Your gradient is 0
Now find the y intercept. This is whrre where the line crosses the y axis, when X = 0
(0,3)
Your y intercept is 3.
Now put It into the formula y = mx + c
m = 0
c = 3
y = 0x + 3
y = 0 + 3
y = 3
