Question: The equation of a line is \( y = \frac{3}{7}x + 5 \). (a) What is the slope of a line parallel…

The equation of a line is \( y = \frac{3}{7}x + 5 \).

(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 \(\boxed{\phantom{0}}\). (Simplify your answer.)

Solution

The equation of the line is given as \( y = \frac{3}{7}x + 5 \). (a) To find the slope of a line parallel to it, we look at the slope of the given line. The slope \( m \) of the line is \( \frac{3}{7} \). Lines that are parallel have the same slope. Therefore, the slope of a line parallel to it is \( \frac{3}{7} \). (b) To find the slope of a line perpendicular to it, we take the negative reciprocal of the slope of the given line. The slope of the given line is \( \frac{3}{7} \). The negative reciprocal of \( \frac{3}{7} \) is \( -\frac{7}{3} \). Therefore, the slope of a line perpendicular to it is \( -\frac{7}{3} \).