Question

The line 2x + 5y + 3 = 0 is perpendicular to y = (5/2)x+ 5. True or False?​

Answer 1

this is Ture

Explanation:

Answer 2

True

Explanation:

By changing both equations to slope-intercept, it is easier to determine whether two lines are perpendicular.

Since
`y = (5)/(2) x+ 5` is already in slope-intercept form, we just need to change the first given equation.

2x + 5y + 3 = 0

2x + 5y = -3

5y = -2x -3

`y=(-2)/(5)x-(3)/(5)`

Two lines are perpendicular when the slope of the lines (coefficient of x) are negative reciprocals (opposite sign of the inverse of a number).

Comparing the two slopes
`(5)/(2)` and
`(-2)/(5)`, we can see they they both fit the criteria of being opposite signs and inverses of each other.

So 2x + 5y + 3 = 0 is perpendicular to y = (5/2)x+ 5.