Answer

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Slope = -2/5 or -0.4
Slope Intercept = y = -2/5x + 1/0.29411764705882
Distance Between Points = 5.3852
Midpoint = (-3/2, 4)
Angle 1 = -21.8014
Angle 2 = 111.8014
Y-intercept = 1/0.29411764705882

↓Steps Explained:↓

Given (-4, 5) and (1, 3)

calculate 8 items:

Calculate the slope and point-slope form:

Slope (m) =	y₂ - y₁
	x₂ - x₁

Slope (m) =	3 - 5
	1 - -4

Slope (m) =	-2
	5

Calculate the point-slope form :

y - y₁ = m(x - x₁)

y - 5 = -2/5(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, 5) and the slope (m) = -2/5

b = 5 - (-2/5 * -4)

b = 5 - (8/5)

b  =   25
   5
-

8
5

b = 17
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 17

Our reduced fraction is:

1
0.29411764705882

Build standard line equation

y = -2/5x + 1/0.29411764705882

Distance between the 2 points

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

D = Square Root((1 - -4)² + (3 - 5)²)

D = Square Root((5² + -2²))

D = √(25 + 4)

D = √29

D = 5.3852

Midpoint between the 2 points

Midpoint =

x₂ + x₁
2

,
y₂ + y₁
2
Midpoint =

-4 + 1
2

,
5 + 3
2

Midpoint =

-3
2

,
8
2

Midpoint = (-3/2, 4)

Form a right triangle

Plot a 3^rd point (1,3)

Our first triangle side = 1 - -4 = 5

Our second triangle side = 5 - 3 = 2

Using the slope we calculated
Tan(Angle1) = -0.4

Angle1 = Atan(-0.4)

Angle1 = -21.8014°

Since we have a right triangle
We only have 90° left
Angle2 = 90 - -21.8014° = 111.8014

Calculate the y intercept of our line

The y intercept is found by
Setting x = 0 in y = -2/5x + 1/0.29411764705882

y = -2/5(0) + 1/0.29411764705882

y = 1/0.29411764705882

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) = (-4,5) + t(1 - -4,3 - 5)

(x,y) = (-4,5) + t(5,-2)

x = -4 + 5t

y = 5 - 2t

Calculate Symmetric Equations:

x - x₀
z

y - y₀
b

Plugging in our numbers, we get:

x - -4
5

y - 5
-2

Plot both points and line on the Cartesian Graph:

Final Answers