Answer:
D. 5x - 3y = 27
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.
[tex]\begin{gathered} A\colon3x-5y=20\implies5y=3x-20\implies y=\frac{3}{5}x-\frac{20}{5} \\ B\colon5x+3y=21\implies3y=-5x+21\implies y=-\frac{5}{3}x+\frac{21}{3} \end{gathered}[/tex]We do likewise for options C and D.
[tex]\begin{gathered} C\colon3x+5y=10\implies5y=-3x+10\implies y=-\frac{3}{5}x+\frac{10}{5} \\ D\colon5x-3y=27\implies3y=5x-27\implies y=\frac{5}{3}x-\frac{27}{3} \end{gathered}[/tex]We can see that option D has a slope of 5/3.
It is the line perpendicular to the line y = - 3/5x + 1.
