This point slope form calculator https://calculator-online.net/point-slope-form-calculator/ finds the formulas of the parametric equation of a straight line and the equation of a straight line with a slope by the coordinates of two points belonging to a straight line.

On this page, you will find two calculators that construct the equation of a line from the coordinates of two points belonging to this line.

The first calculator point slope form equation calculator finds the equation of a straight line with a slope, that is, an equation in the form
y = ax + b.
It also plots and outputs the slope and y- value separately at the intersection of the line with the y-axis.
The second point slope form equation parametric finds the parametric equations of a straight line, that is, a system of equations of form
x = at + x_0
y = bt + y_0
It also plots and outputs the direction vector separately.
Equation of a straight line with a slope at two points:
First Point Second Point
X y x y
6 -2 3 4

Equation of a straight line stop the y-value at the y-intercept
y= - 2 x + 10 -2 10




Parametric equation of a straight line
X y x y
6 -2 3 4

Parametric equation for x parametric equation for y Direction vector
-3
6
x = - 3 t + 6 y= 6 t – 2



Calculation formulas can be found under the Point Slope Form Calculator with Equation & Formula.
Equation of a straight line with a slope
Let us find the equation of a straight line with a point slope form calculator from two known points
(x_0,y_0 )and (x_1,y_1 ).

In this way, we need how to find point slope a and the y coordinate of the point of intersection of the straight line with the ordinate axis b.

We can write the following equations for two points with respect to a and b
y_0= ax_0+ b
y_1= ax_1+ b

Subtract the first from the second
y_1- y_0= ax_1- ax_0+ b – b
y_1- y_0= ax_1- ax_0
y_1- y_0= a (x_1-x_0 )

Where
a = {y_1– y_0 } /{x_1–x_0 }

B can be found as
b = y-ax
Thus, as soon as we have found a, to calculate b, it is enough only to substitute the values x_0,y_0, for x_1,y_1, into the expression above.

Parametric equation of a straight line
Let us find the parametric equation of the straight line from two known points (x0, y0) and (x1, y1).

We need to find the components of the direction vector.

This vector describes the magnitude and direction of imaginary movement along a straight line from the first to the second point.

Having a direction vector, it is easy to write down the parametric equations of a straight
x = d_1t+ x_0
y = d_2t+ y_0
Line. Note that if t = 0, then x = x_0,y = y_0 and if t = 1, then = x_1,y = y_1