Write an equation of the line that passes through the points 5,2 and -5,6

y= -0.40x+ 4.00

Step-by-step explanation:

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

d = √  ((X2-X1)2+(Y2-Y1)2)

d = √(-5-5)2+(6-2)2

d = √((-10)2+(4)2)

d = √(100+16)

d = √116

The distance between the points is 10.770329614269

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=(5+-5)/2=0

Find the Y value of the midpoint

Ym=(Y1+Y2)/2

Ym=(2+6)/2=4

The midpoint is: (0,4)

Graphing the two points, midpoint and distance

P1 (5,2)

P2 (-5,6)

Midpoint (0,4)

The length of the black line is the distance between the points (10.770329614269)

Find the slope of the line connecting the two points

Slope =  (Y2-Y1)  =  (6-2)  =  (4)  = -0.4

(X2-X1)(-5-5)(-10)

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 -0.4

y = -0.40x + b

We substitute x and y for the values from one of our points (5,2)

2 = -.40×5 + b

2 = -2.00 + b

2--2.00 = b

4.00 = b

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

y= -0.40x+ 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= -0.40x+ 4.00

0= -0.40x+ 4.00

0.40x= 4.00

x= 4.00/0.40 = 10.00

The x intercept for this straight line is 10.00

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= -0.40×0+ 4.00

y= 4.00

The y intercept for this straight line is 10.00

21/58.

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