Hi,
I would be grateful if someone could confirm whether the equation of the line perpendicular to the line 10x + 7y = 11 which passes through points (-1, 3) is 7x - 10y = -37?
If not, where have I gone wrong?!
Hello, looking0glass!
You are right!
You can check your own work . . .
You have: .$\displaystyle 7x - 10y \:=\:-37$
Is it perpendicular to $\displaystyle 10x + 7y \:=\:15$?
Solve for $\displaystyle y$ . . .
Their line is: .$\displaystyle y \:=\:\text{-}\tfrac{10}{7}x+\tfrac{15}{7}$
. . Its slope is: $\displaystyle m_1 \:=\:\text{-}\tfrac{10}{7}$
Your line is: .$\displaystyle y \:=\:\tfrac{7}{10}x + \tfrac{37}{10}$
. . Its slope is: $\displaystyle m_2\:=\:\tfrac{7}{10}$
Since $\displaystyle m_1\!\cdot\!m_2 \:=\:-1$, the line are perpendicular.
Does your line pass through (-1, 3) ?
Does (-1,3) satisfy your equation?
. . $\displaystyle 7(-1) - 10(3) \:=\:-37$ . . . Yes!
Therefore, your equation is correct.