Answer:
y = -3x - 1
Step-by-step explanation:
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, (1,-4), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=1 and y1=-4.
Also, let's call the second point you gave, (-2,5), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-2 and y2=5.
To find b, think about what your (x,y) points mean:
(1,-4). When x of the line is 1, y of the line must be -4.
(-2,5). When x of the line is -2, y of the line must be 5.
Because you said the line passes through each one of these two points, right?
Now, look at our line's equation so far: y=-3x+b. b is what we want, the -3 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 (1,-4) and (-2,5).
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:
(1,-4). y=mx+b or -4=-3 × 1+b, or solving for b: b=-4-(-3)(1). b=-1.
(-2,5). y=mx+b or 5=-3 × -2+b, or solving for b: b=5-(-3)(-2). b=-1.
See! In both cases we got the same value for b. And this completes our problem.
