Question

Which of the following lines is perpendicular to the line y = - 3/5x + 1?A. 3x -5y = 20B. 5x + 3y = 21C. 3x + 5y = 10D. 5x - 3y = 27

Answer 1

D. 5x - 3y = 27

Step-by-step explanation:

Definition: Two lines are perpendicular if the product of their slopes is -1.

Given the line: y=- 3/5x + 1

Slope = -3/5

Therefore, the slope of the perpendicular line must be = 5/3.

To determine the perpendicular line, we make y the subject in each equation.

`\begin{gathered} A\colon3x-5y=20\implies5y=3x-20\implies y=(3)/(5)x-(20)/(5) \\ B\colon5x+3y=21\implies3y=-5x+21\implies y=-(5)/(3)x+(21)/(3) \end{gathered}`

We do likewise for options C and D.

`\begin{gathered} C\colon3x+5y=10\implies5y=-3x+10\implies y=-(3)/(5)x+(10)/(5) \\ D\colon5x-3y=27\implies3y=5x-27\implies y=(5)/(3)x-(27)/(3) \end{gathered}`

We can see that option D has a slope of 5/3.

It is the line perpendicular to the line y = - 3/5x + 1.