# Find the Slope, Distance, Angle and Equation of Line

Online calculator to find slope, length/distance, angle and equation of a line segment for entered the coordinates (x_{1}, y_{1}), (x_{2}, y_{2}) of two points.

### Formula :

m = (y_{2}-y_{1}) / (x_{2}-x_{1}) and

Distance = √ ( (x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} )

Angle = arctan ( m ) and

Line of Equation is y = mx + b ,

Where

m = slope

two ponits coordinates are (-4, 3) and (9, 8):

$$\text{find the slop } m = \frac{(y_2 - y_1)}{(x_2 - x_1)}$$ $$ m = \frac{(8 - 3)}{(9 - (-4))}$$ $$ m = \frac{(5)}{(9 + 4)}$$ $$ m = \frac{5}{13}$$ $$ m = 0.3846153846153846$$ $$ m = 0.3846$$

Now find the distance using √ ( (x

_{2}-x

_{1})

^{2}+ (y

_{2}-y

_{1})

^{2}) $$ distance = \sqrt { (x_2 - x_1)^2 + (y_2 - y_1)^2} $$ $$= \sqrt { (9 - (-4))^2 + (8 - 3)^2} $$ $$= \sqrt { (9 + 4)^2 +(8 - 3)^2} $$ $$= \sqrt { (13)^2 + (5)^2} $$ $$= \sqrt {169+ 25} $$ $$= \sqrt {194} $$ $$= 13.928$$

The slop is defined as opposite/adjacent and in trigonometry tan θ = opposite/adjacent, so we can say $$\tan \theta = \frac{opposite}{adjacent} = m$$ $$\tan \theta = m$$ we can find the angle θ using: $$\theta = \arctan(m)$$ $$\theta = \arctan(0.3846)$$ $$\theta = 21.0367$$ This angle is also called inclination of line.

Now we can find a linear equation using following formula:

$$y = mx + b$$ Now we can calculate b. as we already know the slope (0.3846)

The equation can be re-written as:

$$b = y -mx$$ We will take one of the given points (-4, 3) and apply the values in formula.

$$b = 3 -0.3846 \times (-4)$$ $$b = 3 + 1.5384 = 4.5384$$ We can use the other point (9,8) to check the value of b: $$b = 8 -0.3846 \times (9)$$ $$b = 8 - 3.4614 = 4.5386 $$ Now apply the values to the equation : $$y = mx + b$$ $$y = 0.3846 x + 4.5386 $$