Question

Write the equation of the line which passes through (2, –1) and is perpendicular to the line with equation 5y – x = 1.

Answer 1

Solve 5y - x = 1 for y such that y = mx + b so we can extract the slope.
y = 1/5x + 1/5
Perpendicular lines have opposite signed reciprocal slopes.
1/5 would have an opposite signed (-) reciprocal (5) slope of -5

Now let's find b by substituting the values of y, m, and x into y = mx + b:
-1 = -5(2) + b
-1 = -10 + b
9 = b
So the equation is y = -5x + 9 or 5x + y = 9