Find the slope of the line through each pair of points (7, 1 ), (1, -18)

y=-17/6x+125/6

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:

m=m1 - y1

    x2- x1

So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (7,1), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=7 and y1=1.

Also, let's call the second point you gave, (1,18), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=1 and y2=18.

Now, just plug the numbers into the formula for m above, like this:

m= 1 - 18/ 1 - 7

or

      m= 17/ -6

or

      m=

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= x+b

Now, what about b, the y-intercept?

To find b, think about what your (x,y) points mean:

(7,1). When x of the line is 7, y of the line must be 1.

(1,18). When x of the line is 1, y of the line must be 18.

Because you said the line passes through each one of these two points, right?

Now, look at our line's equation so far: y=-17/6x+b. b is what we want, the -17/6 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 specifically passes through the two points (7,1) and (1,18).

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.

(7,1). y=mx+b or 1=-17/6 × 7+b, or solving for b: b=1-

(-17/6)(7). b=125/6.

(1,18). y=mx+b or 18=-17/6 × 1+b, or solving for b: b=18-(-17/6)(1). b=125/6.

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

(7,1) and (1,18)

is

y=-17/6x+125/6

Hope this helps you. x

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hello from mrbilldoesmath!

answer:   x (x+6)^2, choice b

discussion:

factor x out of the equation:

x^3 + 12x^2 + 36x = x (x^2 + 12x + 36).

note that 6+6 = 12 and 6*6 = 36 so the above factors into:

x (x+6)^2

which is choice b

you,

mrb