Answer:
15y + 30x = 16
Explanation:
The first line is 4x - 8y = 0
Convert this to slope-intercept form y = mx + b where m = slope
Multiplying by -1 ==> -4x + 8y = 0
Add -4x to both sides ==> 8y = 4x
Divide both sides by 8
==> y = (4/8)x = (1/2)x (L1)
Slope = 1/2 and y-intercept = 0
Let L2 represent the equation of the line perpendicular to L1
The slope of a line, L2, perpendicular to line L1 will have as its slope the negative of the reciprocal of slope of L1
~ Reciprocal of L1 slope = 1 ÷ 1/2 = 2
~ Negative of reciprocal = -2
Slope of L2 = -2
Equation of L2 is y = -2x + b
To find b, substitute point (x = 1/5, y = 2/3) into L2 equation and solve for b
We get 2/3 = -2(1/5) + b
2/3 = - 2/5 + b
Add 2/5 to both sides
2/3 + 2/5 = -2/5 + 2/5 + b
2/3 + 2/5 = b
or
b = 2/3 + 2/5
Multiply both sides by 15 (LCM of 3 and 5)
15b = 15(2/3) + 15(2/5) = 10 + 6 = 16
15b = 16
b = 16/15
So equation of L2, the line perpendicular to L1 is
y = -2x + 16/15
This is in slope intercept form. We have to convert it to standard form which is Ax + by = C
y = -2x + 16/15
Add 2x to both sides:
y + 2x = 2x - 2x + 16/15 = 16/15
Multiply throughout by 15
==> 15.y + 15.2x =16/15(15)
==> 15y + 30x = 16