Equation of a Line Calculator

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**Step 1 :**

**Step 2 :**

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: (x_{1}, y_{1}) and (x_{2}, y_{2}), 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 - y_{1} = m (x - x_{1}).

where m is the slope and (x_{1}, y_{1}) is any point on the line.

Two Point Form: y - y_{1} = $\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ (x - x_{1})

where (x_{1}, y_{1}) and (x_{2}, y_{2}) 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.

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:

Standard Form

Slope Intercept Form

where m = slope of the line, b is the y - coordinate of the point where the line crosses y-axis.

Point Slope Form

where m is the slope and (x

Two Point Form

where (x

where a is the x-intercept and b is the y-intercept. Slope is -$\frac{b}{a}$.

Observe the given coordinates (x_{1}, y_{1}) and (x_{2}, y_{2}).

Equation of line is given by

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

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

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) = (x

_{1}, y_{1})

(4, 6) = (x

_{2}, y_{2})**Step 2 :**Equation of line is given by

y - y

_{1}= $\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ (x - x_{1})

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

**Answer :**x - y + 2 =0

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) = (x

_{1}, y_{1})

(4, 6) = (x

_{2}, y_{2})**Step 2 :**Equation of line is given by

y - y

_{1}= $\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ (x - x_{1})

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

**Answer :**2x - y - 2 =0

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