Find the equation of a line perpendicular to the line 4y = 7x + 3 which passes through (-3, 1)
-
A.
7y + 4x + 5 = 0 -
B.
7y – 4x – 5 = 0 -
C.
3y – 5x + 2 = 0 -
D.
3y + 5x – 2 = 0
Correct Answer: Option A
Explanation
Equation: 4y = 7x + 3
(implies y = frac{7}{4} x + frac{3}{4})
Slope = coefficient of x = (frac{7}{4})
Slope of perpendicular line = (frac{-1}{frac{7}{4}})
= (frac{-4}{7})
The perpendicular line passes (-3, 1)
(therefore) Using the equation of line (y = mx + b)
m = slope and b = intercept.
(y = frac{-4}{7} x + b)
To find the intercept, substitute y = 1 and x = -3 in the equation.
(1 = frac{-4}{7} (-3) + b)
(1 = frac{12}{7} + b)
(b = frac{-5}{7})
(therefore y = frac{-4}{7} x – frac{5}{7})
(7y + 4x + 5 = 0)
There is an explanation video available below.