tell whether each of the following lies in parallel, perpendicular, or neither to y=-5/3x+3/5

Question

A. 3y=-3x+5

B. 15y=-25x+9

C. y=3/5x-2

D. 5y+3x=15

Answer 1

Hi Lilac,

 

In order to answer the question you must compare the slopes of the lines

 

parallel lines have the same slope

 

perpendicular lines have slopes that are negative reciprocals (when you mutliply them you get -1)

 

otherwise the lines intersect but are not perpendicular

 

so lets find the slope of the lines

 

y =-5/3x + 3/5     Slope is -5/3

 

A. 3y = -3x +5  can be rewritten as y = -x + 5/3   and the slope is -1   (so this is neither

 

B. 15y = -25x + 9 can be rewritten as y = -5/3x + 3/5  (slope is -5/3, so this is the same line

 

C. y = 3/5x - 2       (slope is 3/5   and this is the negative reciprocal of -5/3   so they are perpendicular

 

D.  5y+3x =15

 

5y = -3x + 15   (you can take it from here following the examples above

 

Hope this helps

Answer 2

When in the form y=mx+b, m represents the slope of the line.  Parallel lines have the same slope, and perpendicular ones have negative reciprocal slopes.

 

Step 1, put the lines in the above (slope intercept) form:

 

A. y=-3x/3+5, y=-x+5, slope = -1

B. y=-25x/15+9/15, y=-5x/3+3/5, slope = -5/3

C. y=3x/5-2, slope = 3/5

D. y=-3x/5+15/5, slope = -3/5

 

Since the line in question has a slope of -5/3, we can conclude the following:

 

A. neither

B. parallel

C. perpendicular (3/5 is the negative reciprocal of -5/3)

D. neither (reciprocal, but not negative)