Question

I need to write an equation the Aline’s with the stars so that the purple ball will fall on to the line and hit all the stars

Answer 1

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

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 ) = (- 12, 4 ) and (x₂, y₂ ) = (0, - 5 ) ← coordinates of 2 end stars

m =
`(-5-4)/(0-(-12))` =
`(-9)/(0+12)` =
`(-9)/(12)` = -
`(3)/(4)`

the lowest star is on the y- axis at (0, - 5 ) ⇒ c = - 5

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