Top

Equation of a Line Calculator
Top
The line steepness, incline and grade are described by Slope. If the value of the slope is high, then it indicates steeper incline. The slope of a line can be defined as the ratio of "raise (change in y-axis)" over "run (change in x-axis)" between the points. If the two points are: (x1, y1) and (x2, y2), then it's slope(m) is given by:
Slope(m) = $\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Linear equations also referred as straight line can be written in several different forms:
General Form: Ax + By + C = 0. A $\neq$ 0 and B $\neq$ 0 Slope of the line is -$\frac{A}{B}$

Standard Form
: Ax + By = C.

Slope Intercept Form
: y = mx + b.
where m = slope of the line, b is the y - coordinate of the point where the line crosses y-axis.

Point Slope Form
: y - y1 = m (x - x1).
where m is the slope and (x1, y1) is any point on the line.

Two Point Form
: y - y1 = $\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ (x - x1)
where (x1, y1) and (x2, y2) are two points on the line and $\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ is slope of the line.

Intercept Form: $\frac{x}{a}$ + $\frac{y}{b}$ + 1.
where a is the x-intercept and b is the y-intercept. Slope is -$\frac{b}{a}$.
Equation of Line Calculator is used to calculates the slope and equation of the straight line, when its two end points are given.

## Steps for Equation of a Line Calculator

Step 1 :

Observe the given coordinates (x1, y1) and (x2, y2).

Step 2 :

Equation of line is given by

y - y1 = $\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ (x - x1)

Solve the above equation and convert it into standard form: Ax + By = C

## Problems on Equation of a Line Calculator

1. ### Find the two point slope form for the line which contains coordinates (1, 3) and (4, 6)?

Step 1 :

Given coordinates:

(1, 3) and (4, 6)

(1, 3) = (x1, y1)

(4, 6) = (x2, y2)

Step 2 :

Equation of line is given by

y - y1 = $\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ (x - x1)

y - 3 = $\frac{6 - 3}{4 - 1}$ (x - 1)

y - 3 = $\frac{3}{3}$ (x - 1)

y - 3 = 1(x - 1)

y - 3 = x - 1

x - y + 2 =0

x - y + 2 =0

2. ### Find the two point slope form for the line which contains coordinates (2, 2) and (4, 6)?

Step 1 :

Given coordinates:

(2, 2) and (4, 6)

(2, 2) = (x1, y1)

(4, 6) = (x2, y2)

Step 2 :

Equation of line is given by

y - y1 = $\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ (x - x1)

y - 2 = $\frac{6 - 2}{4 - 2}$ (x - 2)

y - 2 = $\frac{4}{2}$ (x - 2)

y - 2 = 2(x - 2)

y - 2 = 2x - 4

2x - y - 2 =0