Find the equation of a line passing through points (-7, -10) , (-5, -20)

You want to find the equation for a line that passes through the two points:

                          (-7,-10) and (-5,-20).

First of all, remember what the equation of a line is:

                                y = mx+b

here, m is the slope, b 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.

Consider (-7,-10) as point #1, so the x and y numbers given will be called x1 and y1. Or, x1=-7 and y1=-10.

Consider (-5,-20), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-5 and y2=-20.

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

                       m=(-20 - -10)/(-5 - -7)

                                m=-10/2

                                   m=-5

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=-5x+b

Now, what about b, the y-intercept?

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

(-7,-10). When x of the line is -7, y of the line must be -10.

(-5,-20). When x of the line is -5, y of the line must be -20.

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

Now, look at our line's equation so far: y=-5x+b. b is what we want, the -5 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,-10) and (-5,-20).

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,-10). y=mx+b or -10=-5 × -7+b, or solving for b: b=-10-(-5)(-7). b=-45.

(-5,-20). y=mx+b or -20=-5 × -5+b, or solving for b: b=-20-(-5)(-5). b=-45.

See! 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,-10) and (-5,-20) is y=-5x-45.

step-by-step explanation:

milk=16 large

soda=280 kids

juice box=82 regular

63 soda +63 regular

124 large total