Question

the equation of line b is $y = \frac{-9}{4}x + 7$. line c is parallel to line b. what is the slope of line c? simplify your answer and write it as a proper fraction, improper fraction, or integer.

Explanation:

Step1: Recall slope of parallel lines

Parallel lines have equal slopes. The equation of a line in slope - intercept form is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.

Step2: Identify slope of line b

For the line \(y=\frac{- 9}{4}x + 7\), comparing with \(y=mx + b\), the slope \(m\) of line \(b\) is \(\frac{-9}{4}\) (or \(-\frac{9}{4}\)).

Step3: Determine slope of line c

Since line \(c\) is parallel to line \(b\), the slope of line \(c\) is equal to the slope of line \(b\). So the slope of line \(c\) is \(-\frac{9}{4}\).

Answer:

\(-\frac{9}{4}\)