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# Equation of a Line Calculator

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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.

### 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 = 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.

## Steps

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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.

## Problems

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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 $13x - 2y = -49$.