Answer

Success!

Slope = -6/5 or -1.2
Slope Intercept = y = -6/5x + 1/0.051020408163265
Distance Between Points = 7.8102
Midpoint = (11/2, 13)
Angle 1 = -50.1944
Angle 2 = 140.1944
Y-intercept = 1/0.051020408163265

↓Steps Explained:↓

Given (3, 16) and (8, 10)

calculate 8 items:

Calculate the slope and point-slope form:

Slope (m) =	y₂ - y₁
	x₂ - x₁

Slope (m) =	10 - 16
	8 - 3

Slope (m) =	-6
	5

Calculate the point-slope form :

y - y₁ = m(x - x₁)

y - 16 = -6/5(x - 3)

Calculate the line equation

Standard equation of a line is y = mx + b
where m is our slope
x and y are points on the line
b is a constant.

Rearrange the equation to solve for b
we get b = y - mx.
Use (3, 16) and the slope (m) = -6/5

b = 16 - (-6/5 * 3)

b = 16 - (-18/5)

b  =   80
   5
-

-18
5

b = 98
5

Solve for b

This fraction is not reduced. Using our GCF Calculator, we see that the top and bottom of the fraction can be reduced by 98

Our reduced fraction is:

1
0.051020408163265

Build standard line equation

y = -6/5x + 1/0.051020408163265

Distance between the 2 points

D = Square Root((x₂ - x₁)² + (y₂ - y₁)²)

D = Square Root((8 - 3)² + (10 - 16)²)

D = Square Root((5² + -6²))

D = √(25 + 36)

D = √61

D = 7.8102

Midpoint between the 2 points

Midpoint =

x₂ + x₁
2

,
y₂ + y₁
2
Midpoint =

3 + 8
2

,
16 + 10
2

Midpoint =

11
2

,
26
2

Midpoint = (11/2, 13)

Form a right triangle

Plot a 3^rd point (8,10)

Our first triangle side = 8 - 3 = 5

Our second triangle side = 16 - 10 = 6

Using the slope we calculated
Tan(Angle1) = -1.2

Angle1 = Atan(-1.2)

Angle1 = -50.1944°

Since we have a right triangle
We only have 90° left
Angle2 = 90 - -50.1944° = 140.1944

Calculate the y intercept of our line

The y intercept is found by
Setting x = 0 in y = -6/5x + 1/0.051020408163265

y = -6/5(0) + 1/0.051020408163265

y = 1/0.051020408163265

Find the parametric equations for the line

Parametric equations are written as
(x,y) = (x₀,y₀) + t(b,-a)

Plugging in our numbers, we get

(x,y) = (3,16) + t(8 - 3,10 - 16)

(x,y) = (3,16) + t(5,-6)

x = 3 + 5t

y = 16 - 6t

Calculate Symmetric Equations:

x - x₀
z

y - y₀
b

Plugging in our numbers, we get:

x - 3
5

y - 16
-6

Plot both points and line on the Cartesian Graph:

Final Answers