Question

Consider the line - 5x – 3y = 7.

(a) What is the slope of a line parallel to this line?
(b) What is the slope of a line perpendicular to this line?

Answer 1

a: m=5/3

b: m=-3/5

Explanation:

first, before answering the questions, let's change the line from standard form (ax+by=c), where a and b are free coefficients into slope-intercept form (y=mx+b), where m is the slope and b is the y intercept

subtract 5x from both sides

-3y=-5x+7

divide by -3

y=5/3x-7/3

now to answer part a:

parallel lines have the same slopes, but different y intercepts.

the slope of the given line is 5/3, so therefore, a parallel line to the line y=5/3x-7/3 will also be 5/3

part b:

perpendicular lines have slopes that are negative and reciprocal; if you multiply them together, the result is -1

so to find the slope of a perpendicular line, use this formula:

5/3m=-1

multiply by 3/5 to isolate the variable

m=-3/5

therefore the slope of a perpendicular line will be -3/5

hope this helps!