Tell whether the lines are parallel perpendicular or neither

y=-4/5x+3
4x-5y=-15

parallel
perpendicular**
neither

it’s neither πŸ‘©β€β€οΈβ€πŸ’‹β€πŸ‘©

So neither

Let me put on my clown hat and give you a jovial answer! *Puts on clown hat*

Well well, it seems like we have a couple of lines here! One line is telling us the equation y = -4/5x + 3, and the other line says 4x - 5y = -15. So, are these lines parallel, perpendicular, or neither?

Drumroll, please...

*Drumroll noise*

These lines are actually perpendicular! Ta-da! Or, as the cool kids say, perpendicularity strikes again! 🎺

Now go forth and amaze your mathematical friends with your new knowledge!

To determine whether the given lines are parallel, perpendicular, or neither, we need to analyze their slopes. The slope-intercept form of a line is given by y = mx + b, where m represents the slope.

For the first line, y = (-4/5)x + 3, we can identify that the slope, m₁, is -4/5.

For the second line, 4x - 5y = -15, we need to convert it to slope-intercept form. First, isolate y:

4x - 5y = -15
-5y = -4x - 15
Divide through by -5:
y = (4/5)x + 3

Now we can identify the slope, mβ‚‚, as 4/5.

To determine the relationship between the slopes, we can make a comparison:
m₁ = -4/5
mβ‚‚ = 4/5

If the slopes are equal, the lines are parallel.
If the slopes are negative reciprocals of each other, the lines are perpendicular.
If neither of these conditions is met, the lines are neither parallel nor perpendicular.

Comparing the slopes, we can see that m₁ and mβ‚‚ are negative reciprocals of each other, which means the lines are perpendicular.

Nope.

1st has slope -4/5
2nd has slope 4/5

Not negative reciprocals