Equation of a line is also referred as linear equation. A straight line on a x,y plan is described in many different forms. In all the forms, "m", "a" and "b" are slope of the line, x-intercept and y-intercept of the line.

When you plug in the coordinates of two points into the equation of line calculator. The equation of line calculator will determine the slope and equation of a line.

### Various forms of equation of a line are :

**1.Standard form : $Ax + By = C$**

2.Slope-intercept form : $y = mx + b$

3.Point-slope form : $y - y_{1} = m(x - x_{1})$

Here, $(x_{1}, y_{1})$ are the points on the line.

4.Two-point from : $y - y_{1}$ = $\frac{y_{2}-y_{1}}{x_{2}-x_{1}} (x - x_{1})$

Here, $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ is the slope of the equation.

5.Two-intercept form : $\frac{x}{a}$ + $\frac{y}{b}$ = 1

6.Vertical line form : x = a

7.Horizontal line form : y = b2.Slope-intercept form : $y = mx + b$

3.Point-slope form : $y - y_{1} = m(x - x_{1})$

Here, $(x_{1}, y_{1})$ are the points on the line.

4.Two-point from : $y - y_{1}$ = $\frac{y_{2}-y_{1}}{x_{2}-x_{1}} (x - x_{1})$

Here, $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ is the slope of the equation.

5.Two-intercept form : $\frac{x}{a}$ + $\frac{y}{b}$ = 1

6.Vertical line form : x = a

7.Horizontal line form : y = b

When you plug in the coordinates of two points into the equation of line calculator. The equation of line calculator will determine the slope and equation of a line.

**Step 1 :**Put down the coordinates of the two points given in the question.

**Step 2**: To find the slope of the line, apply the formula

m = $\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

**Step 2 :**Substitute the coordinates and slope value into the point-slope form,

$y - y_{1} = m (x - x_{1})$.

Simplify the equation and then bring it into standard form.

Given below are some of the problems based on equation of a line.

### Solved Examples

**Question 1:**Determine the equation of line whose coordinates are (1, 3) and (-2, 5).

**Solution:**

Step 1 : Given coordinates : (1,3) and (-2,5).

$x_{1}$ = 1 ; $x_{2}$ = -2

$y_{1}$ = 3 ; $y_{2}$ = 5

Step 2 : The slope of the line is,

m = $\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

m = $\frac{5 - 3}{-2 - 5}$

m = $\frac{2}{-3}$ = $\frac{-2}{3}$

Step 3 : Equation of a line is,

$y - y_{1} = m (x - x_{1})$

$y - 3$ = $\frac{-2}{3}$ $(x - 1)$

$3(y - 3) = -2(x - 1)$

$3y - 9 = -2x + 2$

$2x + 3y = 11$

Therefore, the equation of line is $2x + 3y = 11$.

**Question 2:**Determine the equation of line whose coordinates are (-3, 5) and (-5, -8).

**Solution:**

Step 1 : Given coordinates : (-3,5) and (-5,-8).

$x_{1}$ = -3 ; $x_{2}$ = -5

$y_{1}$ = 5 ; $y_{2}$ = -8

Step 2 : The slope of the line is,

m = $\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

m = $\frac{-8 - 5}{-5 -(-3)}$

m = $\frac{-13}{-2}$ = $\frac{13}{2}$

Step 3 : Equation of a line is,

$y - y_{1} = m (x - x_{1})$

$y - 5$ = $\frac{13}{2}$ $(x - (-3))$

$2(y - 5) = 13(x + 39)$

$2y - 10 = 13x + 39$

$13x - 2y = -49$

Therefore, the equation of line is $13x - 2y = -49$.