Answer

Success!

Slope = 1/-2 or -0.5
Slope Intercept = y = -1/2x + 6
Distance Between Points = 4.4721
Midpoint = (2, 5)
Angle 1 = -26.5651
Angle 2 = 116.5651
Y-intercept = 6

↓Steps Explained:↓

Given (4, 4) and (0, 6)

calculate 8 items:

Calculate the slope and point-slope form:

Slope (m) =	y₂ - y₁
	x₂ - x₁

Slope (m) =	6 - 4
	0 - 4

Slope (m) =	2
	-4

GCF Calculation

Reduce numerator and denominator by the (GCF) of 2

Slope = (2/2)/(-4/2)

Slope =	1
	-2

Calculate the point-slope form :

y - y₁ = m(x - x₁)

y - 4 = -1/2(x - 4)

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 (4, 4) and the slope (m) = -1/2

b = 4 - (-1/2 * 4)

b = 4 - (4/-2)

b  =   -8
   -2
-

4
-2

b = 12
2

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 12

Our reduced fraction is:

1
0.16666666666667

Build standard line equation

y = -1/2x + 6

Distance between the 2 points

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

D = Square Root((0 - 4)² + (6 - 4)²)

D = Square Root((-4² + 2²))

D = √(16 + 4)

D = √20

D = 4.4721

Midpoint between the 2 points

Midpoint =

x₂ + x₁
2

,
y₂ + y₁
2
Midpoint =

4 + 0
2

,
4 + 6
2

Midpoint =

4
2

,
10
2

Midpoint = (2, 5)

Form a right triangle

Plot a 3^rd point (4,4)

Our first triangle side = 4 - 0 = 4

Our second triangle side = 6 - 4 = 2

Using the slope we calculated
Tan(Angle1) = -0.5

Angle1 = Atan(-0.5)

Angle1 = -26.5651°

Since we have a right triangle
We only have 90° left
Angle2 = 90 - -26.5651° = 116.5651

Calculate the y intercept of our line

The y intercept is found by
Setting x = 0 in y = -1/2x + 6

y = -1/2(0) + 6

y = 6

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) = (4,4) + t(0 - 4,6 - 4)

(x,y) = (4,4) + t(-4,2)

x = 4 - 4t

y = 4 + 2t

Calculate Symmetric Equations:

x - x₀
z

y - y₀
b

Plugging in our numbers, we get:

x - 4
-4

y - 4
2

Plot both points and line on the Cartesian Graph:

Final Answers