Determine the equation for this line, passing through the y int of the line defined by 2x+3y-18=0 and perpendicular to 4x-9y=27.
How would you approach this (we are doing perpendicular and parallel lines)
To approach this problem, use the general form of equation of line:
y = mx + b, where m is the slope of line, b is the y intercept
and use the fact that product of slopes of two perpendicular lines is -1.
Converting the first equation to the standard format, we get:
2x+3y-18 = 0
or y = (-2/3)x + 6
here, y-intercept is 6. so our desired line passes through the point defined by coordinates (0,6).
The second line's equation can similarly be reworked.
4x-9y = 27
or y =(4/9)x - 3
slope of line = 4/9
slope of the desired line = -1/slope of given line = -1 /(4/9) = -9/4
Now we can find the equation of line with slope (-9/4) and passing through (0,6).
y = mx+b = (-9/4)x+b
This line passes through (0,6), so we can substitute x=0 and y=6 in the equation to get b,
b = 6
thus the equation of line is y= (-9/4) x +6
or simplifying to get