Question
Line s has a slope of –5/3. Line t is perpendicular to s. What is the slope of line t? Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answers
GPT-4o mini
To find the slope of line \( t \) which is perpendicular to line \( s \), we need to use the property that the slopes of two perpendicular lines are negative reciprocals of each other.
Given that the slope of line \( s \) is \( -\frac{5}{3} \), we can find the slope of line \( t \) using the formula for the negative reciprocal:
\[
\text{slope of line } t = -\frac{1}{\text{slope of line } s}
\]
Substituting the slope of line \( s \):
\[
\text{slope of line } t = -\frac{1}{-\frac{5}{3}} = \frac{3}{5}
\]
Therefore, the slope of line \( t \) is
\[
\boxed{\frac{3}{5}}.
\]
Given that the slope of line \( s \) is \( -\frac{5}{3} \), we can find the slope of line \( t \) using the formula for the negative reciprocal:
\[
\text{slope of line } t = -\frac{1}{\text{slope of line } s}
\]
Substituting the slope of line \( s \):
\[
\text{slope of line } t = -\frac{1}{-\frac{5}{3}} = \frac{3}{5}
\]
Therefore, the slope of line \( t \) is
\[
\boxed{\frac{3}{5}}.
\]