Answer

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Slope = -3000/1 or -3000
Slope Intercept = y = -3000x + 45000
Distance Between Points = 3000.0002
Midpoint = (3/2, 40500)
Angle 1 = -89.9809
Angle 2 = 179.9809
Y-intercept = 45000

↓Steps Explained:↓

Given (1, 42000) and (2, 39000)

calculate 8 items:

Calculate the slope and point-slope form:

Slope (m) =	y₂ - y₁
	x₂ - x₁

Slope (m) =	39000 - 42000
	2 - 1

Slope (m) =	-3000
	1

Slope = -3000

Calculate the point-slope form :

y - y₁ = m(x - x₁)

y - 42000 = -3000(x - 1)

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 (1, 42000) and the slope (m) = -3000

b = 42000 - (-3000 * 1)

b = 42000 - 3000

b = 45000
1

Solve for b

b = 45000

Build standard line equation

y = -3000x + 45000

Distance between the 2 points

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

D = Square Root((2 - 1)² + (39000 - 42000)²)

D = Square Root((1² + -3000²))

D = √(1 + 9000000)

D = √9000001

D = 3000.0002

Midpoint between the 2 points

Midpoint =

x₂ + x₁
2

,
y₂ + y₁
2
Midpoint =

1 + 2
2

,
42000 + 39000
2

Midpoint =

3
2

,
81000
2

Midpoint = (3/2, 40500)

Form a right triangle

Plot a 3^rd point (2,39000)

Our first triangle side = 2 - 1 = 1

Our second triangle side = 42000 - 39000 = 3000

Using the slope we calculated
Tan(Angle1) = -3000

Angle1 = Atan(-3000)

Angle1 = -89.9809°

Since we have a right triangle
We only have 90° left
Angle2 = 90 - -89.9809° = 179.9809

Calculate the y intercept of our line

The y intercept is found by
Setting x = 0 in y = -3000x + 45000

y = -3000(0) + 45000

y = 45000

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) = (1,42000) + t(2 - 1,39000 - 42000)

(x,y) = (1,42000) + t(1,-3000)

x = 1 + t

y = 42000 - 3000t

Calculate Symmetric Equations:

x - x₀
z

y - y₀
b

Plugging in our numbers, we get:

x - 1
1

y - 42000
-3000

Plot both points and line on the Cartesian Graph:

Final Answers