Answer:
The slope of this line is 1 and the equation for the line is y=x+1
Step-by-step explanation:
So take 2 points passing through the the line (0,1), (-1,0)
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...
So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (0,1), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=0 and y1=1.
Also, let's call the second point you gave, (-1,0), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-1 and y2=0.
Now, just plug the numbers into the formula for m above, like this:
m=
0 - 1
-1 - 0
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:
(0,1). When x of the line is 0, y of the line must be 1.
(-1,0). When x of the line is -1, y of the line must be 0.
Because you said the line passes through each one of these two points, right?
Now, look at our line's equation so far: y=x+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 (0,1) and (-1,0).
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:
(0,1). y=mx+b or 1=1 × 0+b, or solving for b: b=1-(1)(0). b=1.
(-1,0). y=mx+b or 0=1 × -1+b, or solving for b: b=0-(1)(-1). b=1.
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
(0,1) and (-1,0)
is
y=x+1
