Question

Directions – Determine if the two lines are parallel, perpendicular, or intersecting (neither). If necessary, convert each equation to slope-intercept form (y = mx + b). ​ L1: 4x+5y=15 L2: 4y=5x−12

Answer 1

Perpendicular

Explanation:

First note:

• Parallel lines have equal slope
• Perpendicular lines have slopes that are negative reciprocal to each other

Lets check, first we need to convert them to slope intercept form (y = mx + b), where m would be the slope.

L1:

4x + 5y = 15

5y = -4x + 15

y = -4/5x + 3

L2:

4y = 5x - 12

y = 5/4x - 3

Slope of L1 is -4/5 and Slope of L2 is 5/4

Are they negative reciprocals of each other? Yes, because multiplying the slopes would give us "-1"

`-(4)/(5)*(5)/(4)=-1`

So the lines are Perpendicular