I have given this example: Which of the following lines is perpendicular to the line given by the equation 5x − 3y = 2?
a) Line specified parametrically x = 2 + 5s, y = −1−3s, s∈R.
b) The line given by the equation 3x + 5y = −1
c) The line given by the equation 3x + 5y = 1.
d) Line entered parametrically x = 2 + 3s, y = −1 + 5s, s∈R.
I know that the parametric line is given by means of a perpendicular vector, so the vector perpendicular to the line will be in the form (3, 5) in the general form and (5, -3) in the birch, I would conclude that d will be false, but I do not know how dake to continue. Thank you in advance for your advice.
Line $5x-3y=3$ has slope $5/3$ using form $y=mx+c$ for the line where $m$ is the slope, so perpendicular line should have slope $-3/5$, therefore is of the form $3x+5y=k$ for any constant $k$.
Therefore,