Question

line m has a y - intercept of c and a slope of \\(\frac{p}{q}\\), where \\(p \
eq 0\\), \\(q > 0\\), and \\(p \
eq q\\). what is the slope of a line that is parallel to line m?\
\
a. \\(-\frac{p}{q}\\)\
b. \\(\frac{p}{q}\\)\
c. \\(\frac{q}{p}\\)\
d. \\(-\frac{q}{p}\\)

Explanation:

Step1: Recall the property of parallel lines

Parallel lines have equal slopes. This is a fundamental property in coordinate geometry (part of Geometry subfield of Mathematics). So if line \( m \) has a slope of \( \frac{p}{q} \) (assuming the slope of line \( m \) is \( \frac{p}{q} \) from the context, maybe a typo in the original problem but the key is parallel lines have same slope), then a line parallel to \( m \) will have the same slope.

Step2: Identify the correct option

Among the options, the one with slope \( \frac{p}{q} \) (assuming option B is \( \frac{p}{q} \), since the options are about slope of parallel line) should be the answer as parallel lines have equal slopes.

Answer:

B. \( \frac{p}{q} \) (assuming the slope of line \( m \) is \( \frac{p}{q} \) and parallel lines have equal slopes)