$\leftarrow \quad$ The equation of a line is $y=\frac{2}{9} x+7$.
(a) What is the slope of a line parallel to it?
(b) What is the slope of a line perpendicular to it?
(a) The slope of a line parallel to it is $\frac{2}{9}$. (Simplify your answer.)
(b) The slope of a line perpendicular to it is $\square$. (Simplify your answer.)
Answer
Thus, the slope of a line perpendicular to the given line is \(\boxed{-4.5}\).
Step 1 ：The equation of a line is given as \(y=\frac{2}{9} x+7\).
Step 2 ：We are asked to find the slope of a line perpendicular to the given line.
Step 3 ：The slope of a line perpendicular to a given line can be found by taking the negative reciprocal of the slope of the given line.
Step 4 ：The slope of the given line is \(\frac{2}{9}\).
Step 5 ：So, the slope of a line perpendicular to it is \(-\frac{1}{\frac{2}{9}}\).
Step 6 ：Calculating the above expression, we get -4.5.
Step 7 ：Thus, the slope of a line perpendicular to the given line is \(\boxed{-4.5}\).
