Question

finnd the equation of straight line passing through the point (3a,0) and (0,3b) also shwo that the line passese throught the poinits (a , 2b)

Answer 1

see explanation

Explanation:

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 ) = (3a, 0 ) and (x₂, y₂ ) = (0, 3b )

m =
`(3b-0)/(0-3a)` =
`(3b)/(-3a)` = -
`(b)/(a)`

the line crosses the y- axis at (0, 3b ) ⇒ c = 3b

y = -
`(b)/(a)` x + 3b ← equation of line

to show that (a, 2b ) lies on the line , substitute x = a into the equation and if y = 2b then the point lies on the line

y = -
`(b)/(a)` (a) + 3b = - b + 3b = 2b

then the line passes through the point (a, 2b )