# Line slope calculator 5x+6y=75

**Straight line given by points A[3; 10] and B[9; 5]**

## Calculation:

**Slope-intercept form of line:**y = -0.8333x+12.5

**Canonical form of the line equation:**5x+6y-75 = 0

**Parametric form of the line equation:**

x = 6t+3

y = -5t+10 ; t ∈ R

**Slope:**m = -0.8333

**Slope angle of line: φ =**-39°48'20″ = -0.6947 rad

**X intercept:**x

_{0}= 15

**Y intercept:**y

_{0}= q = 12.5

**Distance line from the origin:**d

_{0}= 9.6028

**The length of the segment AB: |AB| =**7.8102

**Vector: AB =**(6; -5)

**Normal vector: n =**(5; 6)

**Midpoint of the segment AB: M =**[6; 7.5]

**Perpendicular Bisector equation:**6x-5y+1.5 = 0

**Vector OA = (3; 10) ; |OA| = 10.4403**

**Vector OB = (9; 5) ; |OB| = 10.2956**

**Scalar product OA .OB = 77**

**Angle ∠ AOB = 44°14'46″ = 0.7722 rad**