Calculus Question: Equations of Lines in 2-Space

[Buzzlastyear]

Homework Statement

A line passes through the point (1, -4) and is perpendicular to the line 3x + 2y – 6 = 0. Determine a scalar equation for the line.

Was also given this: Find a vector which is normal to the line and then use the dot product of this vector and P0P.

Homework Equations

scalar equation: ax+by+c=0

The Attempt at a Solution

i'm not sure if this gets me anywhere but i turned the scalar equation into a vector equation:
Random point on line: (0,-3), therefore vector equation r=(0,-3)+t(2,-3)
Not sure where i can go from here, i just know i have to find a line perpendicular to 3x + 2y - 6 =0 that goes through the point (1, -4)

Homework Statement

Homework Equations

The Attempt at a Solution

 

[LCKurtz]

Remember that a the coefficients of 3x+2y=6 give you a normal vector to the line. So use <3,2> for your direction vector and (1,-4) for your point. Write the vector equation using those and eliminate the parameter to get your scalar equation.

 

[Buzzlastyear]

Okay thank you very much