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

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Given (-4, 5) and (7, -3)

calculate 8 items:

Calculate the slope and point-slope form:

Calculate the point-slope form :

y - y₁ = m(x - x₁)

y - 5 = -8/11(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) = -8/11

b = 5 - (-8/11 * -4)

b = 5 - (32/11)

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 23

Our reduced fraction is:

Build standard line equation

y = -8/11x + 1/0.47826086956522

Distance between the 2 points

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

D = Square Root((7 - -4)² + (-3 - 5)²)

D = Square Root((11² + -8²))

D = √(121 + 64)

D = √185

D = 13.6015

Midpoint between the 2 points

Midpoint = (3/2, 1)

Form a right triangle

Plot a 3^rd point (7,-3)

Our first triangle side = 7 - -4 = 11

Our second triangle side = 5 - -3 = 8

Using the slope we calculated
Tan(Angle1) = -0.72727272727273

Angle1 = Atan(-0.72727272727273)

Angle1 = -36.0274°

Since we have a right triangle
We only have 90° left
Angle2 = 90 - -36.0274° = 126.0274

Calculate the y intercept of our line

The y intercept is found by
Setting x = 0 in y = -8/11x + 1/0.47826086956522

y = -8/11(0) + 1/0.47826086956522

y = 1/0.47826086956522

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(7 - -4,-3 - 5)

(x,y) = (-4,5) + t(11,-8)

x = -4 + 11t

y = 5 - 8t

Calculate Symmetric Equations:

Plugging in our numbers, we get:

Plot these points on the Cartesian Graph:

Final Answers