Line Equation-Slope-Distance-Midpoint-Y intercept Calculator

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

calculate 8 items:

Calculate the slope and point-slope form:

GCF Calculation

Reduce numerator and denominator by the (GCF) of 2

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

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)

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:

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 = (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:

Plugging in our numbers, we get:

Plot both points and line on the Cartesian Graph:

Final Answers