Question

How do you determine if 5y+3x=1 is parallel, perpendicular to neither to the line y+10x=−3?

Answer 1

The 1st equation : 3x+5y=1 or y=(-3/5)x+ 1/5

The 2nd equation : 10x+y=-3 or y=(-10)x+ (-3)

Now, comparing both the equations of the lines with the standard equation of line, y=mx+c, which m is the slope and c is the y-intercept.

We get, slope of first line: (-3/5) = m1.

slope of the second line: (-10) = m2.

Now, for parallelism, m1= m2.

for perpendicularity, m1*m2= -1.

Otherwise, lines are neither parallel nor perpendicular(skew lines).

So for this question, m1*m2 = 6.

So the lines are neither parallel nor perpendicular.