91Ó°ÊÓ

The slope-intercept form of the line is:

$y=mx+c$, where$m$ is the slope of the line and$c$ is the $y$-intercept of the line.

Compare the equation of the line$y=\frac{3}{5}x−3$ with the equation $y=mx+c$.

Therefore, it is obtained that:

$m=\frac{3}{5}$.

Therefore, the slope of the line$y=\frac{3}{5}x−3$ is $\frac{3}{5}$.

Compare the equation of the line$y=\frac{−5}{3}x+2$ with the equation $y=mx+c$.

Therefore, it is obtained that:

$m=\frac{−5}{3}$.

Therefore, the slope of the line$y=\frac{−5}{3}x+2$ is $\frac{−5}{3}$.

Compare the equation of the linerole="math" localid="1647684612244" $y=\frac{5}{3}x−2$ with the equation $y=mx+c$.

Therefore, it is obtained that:

$m=\frac{5}{3}$.

Therefore, the slope of the line$y=\frac{5}{3}x−2$ is $\frac{5}{3}$.

Compare the equation of the line$y=−\frac{3}{5}x+2$ with the equation $y=mx+c$.

Therefore, it is obtained that:

$m=−\frac{3}{5}$.

Therefore, the slope of the line$y=−\frac{3}{5}x+2$ is $−\frac{3}{5}$.

Compare the equation of the line$y=\frac{3}{5}x−2$ with the equation $y=mx+c$.

Therefore, it is obtained that:

$m=\frac{3}{5}$.

Therefore, the slope of the line$y=\frac{3}{5}x−2$ is $\frac{3}{5}$.

Now it can be noticed that:

role="math" localid="1647685192826" $\begin{array}{c}\text{slopeofline}\left(y=\frac{3}{5}x−3\right)×\text{slopeofline}\left(y=\frac{−5}{3}x+2\right)=\frac{3}{5}×\frac{−5}{3}\\ =−1\end{array}$

role="math" localid="1647685283444" $\begin{array}{c}\text{slopeofline}\left(y=\frac{3}{5}x−3\right)×\text{slopeofline}\left(y=−\frac{3}{5}x+2\right)=\frac{3}{5}×\frac{−3}{5}\\ =\frac{−9}{25}\end{array}$

role="math" localid="1647685390939" $\begin{array}{c}\text{slopeofline}\left(y=\frac{3}{5}x−3\right)×\text{slopeofline}\left(y=\frac{3}{5}x−2\right)=\frac{3}{5}×\frac{3}{5}\\ =\frac{9}{25}\end{array}$

It is known that if the two lines are perpendicular then the product of the slopes of the lines is $−1$.

It can be noticed as the product of the slopes of the lines $y=\frac{3}{5}x−3$and $y=\frac{−5}{3}x+2$is $−1$. Therefore the lines $y=\frac{3}{5}x−3$and $y=\frac{−5}{3}x+2$are perpendicular.

Therefore, the equation of a line which is perpendicular to the line $y=\frac{3}{5}x−3$is $y=\frac{−5}{3}x+2$. Therefore, the option A is correct.