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)?

1 Answer
Jun 10, 2016

#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#