Question

The points​ A(0,5), B(4,2), and​ C(0,2) form the vertices of a right triangle in the coordinate plane. What is the equation of the line that forms the​ hypotenuse

Answer 1

y = -
`(3)/(4)` x + 5

Explanation:

the hypotenuse is the line AB

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = A (0, 5 ) and (x₂, y₂ ) = B (4, 2 )

m =
`(2-5)/(4-0)` =
`(-3)/(4)` = -
`(3)/(4)`

the line AB crosses the y- axis at A (0, 5 ) ⇒ c = 5

y = -
`(3)/(4)` x + 5 ← equation of hypotenuse