Answer:
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!