Question

Line b has a slope of –7/5. Line
c is perpendicular to b. What is the slope of line c? Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answer 1

To find the slope of line c, which is perpendicular to line b, we need to use the fact that the product of the slopes of two perpendicular lines is -1.

Given that the slope of line b is \(-\frac{7}{5}\), we can denote the slope of line c as \(m_c\).

We set up the equation:

\[
m_b \cdot m_c = -1
\]

Substituting the slope of line b:

\[
-\frac{7}{5} \cdot m_c = -1
\]

To solve for \(m_c\), we can multiply both sides by \(-1\):

\[
\frac{7}{5} \cdot m_c = 1
\]

Now we isolate \(m_c\) by multiplying both sides by the reciprocal of \(\frac{7}{5}\), which is \(\frac{5}{7}\):

\[
m_c = 1 \cdot \frac{5}{7} = \frac{5}{7}
\]

Thus, the slope of line c is:

\[
\boxed{\frac{5}{7}}
\]