Question

How do you find a standard form equation for the line with the same x intercept as `9x - 2y + 18 = 0` and through the point (4,-5)?

Answer 1

`y = -5/6 -1 2/3`

Explanation:

First we have to find the `x`-intercept of the given line.
To find an `x` intercept, make `y = 0`

`9x - 2(0) + 18 = 0 " " rArr 9x = -18`

`x = -2` is the x-intercept. the coordinates are `(-2, 0)`

Now we have 2 points : `(-2, 0) and (4, -5)`

Now you can use the method of finding the slope and substitute to find c,
However a quicker and easier method if you have 2 points is using the formula:

`(y - y_1)/(x - x_1) = (y_2 - y_1)/(x_2 - x_1)`

`(y - (-5))/(x - 4) = ( 0 - (-5))/((-2) - 4)`

`(y + 5)/(x - 4) = 5/(-6) = -5/6 " now cross multiply"`

`6y + 30 =-5x +20 " simplify and make y = ..."`

`6y = -5x -10`

`y = -5/6 - 10/6 " "rArr y = -5/6 -1 2/3`