Answer:
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