What is the distance between the points (2, 8) and (-6, -7)?

answer:

Step-by-step explanation:Finding the distance, midpoint, slope, equation and the x y-intercepts of a line passing between the two points p1 (2,8) and p2 (-6,-7)

The distance (d) between two points (x1,y1) and (x2,y2) is given by the formula

d = √  ((X2-X1)2+(Y2-Y1)2)

d = √(-6-2)2+(-7-8)2

d = √((-8)2+(-15)2)

d = √(64+225)

d = √289

The distance between the points is 17

The midpoint of two points is given by the formula

Midpoint= ((X1+X2)/2,(Y1+Y2)/2)

Find the x value of the midpoint

Xm=(X1+X2)/2

Xm=(2+-6)/2=-2

Find the Y value of the midpoint

Ym=(Y1+Y2)/2

Ym=(8+-7)/2=0.5

The midpoint is: (-2,0.5)

Graphing the two points, midpoint and distance

P1 (2,8)

P2 (-6,-7)

Midpoint (-2,0.5)

The length of the black line is the distance between the points (17)

Find the slope of the line connecting the two points

Slope =  (Y2-Y1)  =  (-7-8)  =  (-15)  = 1.875

(X2-X1)(-6-2)(-8)

Find the equation of the line passing through the two points

The general equation for a straight line is

y = mx + b

Where m represents the slope of the line which we found in the previous step to be 1.875

y = 1.88x + b

We substitute x and y for the values from one of our points (2,8)

8 = 1.88×2 + b

8 = 3.75 + b

8-3.75 = b

4.25 = b

Knowing both b and m, we can contruct the equation of the line

y= 1.88x+ 4.25

X and Y intercepts

The x-intercept is a point on the graph where y is zero

Using the equation we found in the previous step and substituting zero for y

y= 1.88x+ 4.25

0= 1.88x+ 4.25

-1.88x= 4.25

x= 4.25/-1.88 = -2.27

The x intercept for this straight line is -2.27

The y-intercept is a point on the graph where x is zero

Using the equation we found in the previous step and substituting zero for x

y= 1.88×0+ 4.25

y= 4.25

The y intercept for this straight line is -2.27

your exact question is kind of difficult to understand, so maybe an example will explain what you're supposed to do? i'll work through the first problem on the worksheet.

suppose you have a tray of 652 brownies, and you have 5 friends that you want to feed without picking favorites. how many brownies can you dole out to each of your friends in equal amounts? how many will be left over for you to eat?

what you're doing here is finding a way to arrange the number 652 as the sum of integer multiple of 5 and some remainder:

here ("q" for quotient) is the number of brownies each of your friends get, and is the remainder. that's the basic idea behind division.

we break up the number 652 into parts so that the leading digit stands on its own:

652 = 600 + 52

first we check if it's possible to hand out exactly 100 brownies to each friend. with 5 friends, this means we want to know if we can take out 500 brownies from the tray. we can do this 1 time because we have 600 brownies to take from, and when we do that we're left with 100 + 52 brownies to divvy up. so we know that

652 = 1*500 + 152

next we want to know if it's possible to hand out exactly 10 brownies per friend. if we can, we have to remove 50 brownies from the tray each time until we can't. we have 152 brownies left, and we know that 3(50) = 150, so

152 = 3*50 + 2

now we have 2 brownies left in the tray. is it possible to hand 1 out to each of your 5 friends? no, you'd need a minimum of 5 brownies to do that. so the last 2 are yours.

putting everything together, we found that

652 = 1*500 + 3*50 + 2

and we can rearrange this to write

652 = 5*100 + 5*30 + 2

652 = 5(100 + 30) + 2

652 = 5*130 + 2

so and .

you might be more accustomed to the table depicting the algorithm. that's just a compact way of organizing what we've done above. you can consult the image i've attached below.