Question

Give the slope of each line and then determine whether the two lines are parallel,perpendicular,or neither Parallel nor perpendicular 4x+5y=15

12x+15y=0

Answer 1

First, put the equations into slope-intercept form(y = mx + b):

`4x+5y=15\\5y=-4x+15\\y=(-4)/(5)x+3\\\\ 12x+15y=0 \\15y=-12x\\ y= (-12)/(15)x=(-4)/(5)x\\ y=(-4)/(5)x`
Since slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept, the slope of the line(value of m) determines whether the lines are parallel or perpendicular.
Parallel lines have the same slope, and since
`(-4)/(5)=(-4)/(5)`, the lines are parallel. Also, because the m's aren't the same, the lines aren't identical.

Your answer is parallel.