Find the equation of a straight line passing through
points (h,0)and (0,k) if the point (3,3) lies on the same line
prove
that 1/h+1/k=1/3

see explanation

Step-by-step 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 = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (h, 0) and (x₂, y₂ ) = (0, k)

m = = -

note the line crosses the y- axis at (0, k) ⇒ c = k

y = - x + k ← equation of line

Given that (3, 3) lies on the line then

3 = - + k ( add to both sides )

3 + = k ( multiply through by h to clear the fraction )

3h + 3k = hk ← factor out 3 on the left side

3(h + k) = hk ← divide both sides by hk )

= 1 ( divide both sides by 3 )

= , that is

+ =

+ = ← as required