Answer

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Slope = 1/2 or 0.5
Slope Intercept = y = 1/2x + 1/0.28571428571429
Distance Between Points = 4.4721
Midpoint = (3, 5)
Angle 1 = 26.5651
Angle 2 = 63.4349
Y-intercept = 1/0.28571428571429

↓Steps Explained:↓

Given (1, 4) and (5, 6)

calculate 8 items:

Calculate the slope and point-slope form:

Slope (m) =	y₂ - y₁
	x₂ - x₁

Slope (m) =	6 - 4
	5 - 1

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

b = 4 - (1/2 * 1)

b = 4 - (1/2)

b  =   8
   2
-

1
2

b = 7
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 7

Our reduced fraction is:

1
0.28571428571429

Build standard line equation

y = 1/2x + 1/0.28571428571429

Distance between the 2 points

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

D = Square Root((5 - 1)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 =

1 + 5
2

,
4 + 6
2

Midpoint =

6
2

,
10
2

Midpoint = (3, 5)

Form a right triangle

Plot a 3^rd point (5,4)

Our first triangle side = 5 - 1 = 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° = 63.4349

Calculate the y intercept of our line

The y intercept is found by
Setting x = 0 in y = 1/2x + 1/0.28571428571429

y = 1/2(0) + 1/0.28571428571429

y = 1/0.28571428571429

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) = (1,4) + t(5 - 1,6 - 4)

(x,y) = (1,4) + t(4,2)

x = 1 + 4t

y = 4 + 2t

Calculate Symmetric Equations:

x - x₀
z

y - y₀
b

Plugging in our numbers, we get:

x - 1
4

y - 4
2

Plot both points and line on the Cartesian Graph:

Final Answers