2x-5y=-3 5x+2y=6?

Question

determine whether lines are perpendicular lines

Answer 1

Hey there!

Two lines are perpendicular, when their slopes are negative recriprocal to each other.

Here's the first answer.

2x-5y=-3 --> Write the problem.
-5y=-3-2x --> Subtract 2x on both sides of the equation.
5y=2x+3 --> Divide both sides of the equation by -1.
y=(2x+3)/5 Divide both sides of the equation by 5.

So the slope of the first problem is 2/5 and the equation is y=2/5x+3/5.

Here's the second answer.

5x+2y=6 --> Write the problem.
2y=6-5x --> Subtract both sides of the equation by 5x.
y=(6-5x)/2 Divide both sides of the equation by 2.

So the slope of the second problem is -5/2 and the equation is y=-5x/2+3.

Since -5/2 and 2/5 are both negative recriprocals to each other, the lines are perpendicular.

Hope it helps!

Answer 2

Yep
The slope of a line determines whether or not it is perpendicular to another line--if you move these back into y = mx + b form you will find out they are perpendicular
2x - 5y + -3
-5y = -2x - 3
y = (2/5)x -3 m=(2/5)

5x + 2y = 6
2y = -5x + 6
y = (-5/2)x + 6 m=(-5/2)

So since the slope of the first equation is 2/5 & the reciprocal of that is -5/2, the two lines are perpendicular

Answer 3

Line 1
5y = 2x + 3
y = (2/5)x + 3/5
m1 = 2/5

Line 2
2y = - 5x + 6
y = (- 5/2) x + 3
m2 = (- 5/2)

m1 x m2 = (2/5) x (- 5/2) = - 1

Lines are perpendicular.

Answer 4

2x-5y=-3, its slope=2/5
5x+2y=6, its slope=-5/2
product of slopes=-1,
so these lines are perpendicular.

Answer 5

-5y=-2x-3 y=2/5x+3/5

2y=5x+6 y=-5/2x+6

1/-m is perp lines are perp