Question

What is the equation of a line that passes through the point (10, 5) and is perpendicular to the line whose equation is y=5/4 x-2?

Answer 1

Hey there :)


`y = (5)/(4)x - 2`
Slope is the coefficient of x ⇒
`(5)/(4)`

If the second line is perpendicular to the given line, then the slope of the 2nd line is the reverse/reciprocal of the 1st line ⇒
`(4)/(5)`

(10, 5)
↑ ↑
x₁ y₁

Point-slope form is ( y - y₁ ) = m ( x - x₁ )

y - 4 =
`(4)/(5)` ( x - 10 )
y - 4 =
`(4)/(5) x` - 8

y =
`(4)/(5) x - 4` ⇔ The equation of the line that passes through the point (10,5) ans perpendicular to the given line

Answer 2

Question with point (10,5)

y=-4/5x+13

Slope of the perpendicular line would be the NEGATIVE reciprical!

Explanation:

The answer above is good (except for forgetting it is the negative reciprical) and the person used the point (10,4) not (10,5) from the question...