Find the distance between the points given.
(-3, -6) аnd (3, 2)
52
4
10

4

Step-by-step explanation:

Finding the distance, midpoint, slope, equation and the x y-intercepts of a line passing between the two points p1 (-3,6) and p2 (3,2)

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

d = √  ((X2-X1)2+(Y2-Y1)2)

d = √(3--3)2+(2-6)2

d = √((6)2+(-4)2)

d = √(36+16)

d = √52

The distance between the points is 7.21110255092798

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=(-3+3)/2=0

Find the Y value of the midpoint

Ym=(Y1+Y2)/2

Ym=(6+2)/2=4

The midpoint is: (0,4)

Graphing the two points, midpoint and distance

P1 (-3,6)

P2 (3,2)

Midpoint (0,4)

The length of the black line is the distance between the points (7.21110255092798)

Find the slope of the line connecting the two points

Slope =  (Y2-Y1)  =  (2-6)  =  (-4)  = -0.666666666666667

(X2-X1)(3--3)(6)

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 -0.666666666666667

y = -0.67x + b

We substitute x and y for the values from one of our points (-3,6)

6 = -.67×-3 + b

6 = 2.00 + b

6-2.00 = b

4.00 = b

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

y= -0.67x+ 4.00

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= -0.67x+ 4.00

0= -0.67x+ 4.00

0.67x= 4.00

x= 4.00/0.67 = 6.00

The x intercept for this straight line is 6.00

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= -0.67×0+ 4.00

y= 4.00

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