Answer:
y = 3x - 30
Explanation:
First, put both equations into slope-intercept form.
x + 3y - 4 = 0
3y = -x + 4
y = (-1/3)x + (4/3)
2x + 5y - 20 = 0
5y = -2x + 20
y = (-2/5)x + 4
For a line to be perpendicular to y = (-1/3)x + (4/3), its slope should be the opposite and reciprocal of this line's slope.
The slope of y = (-1/3)x + (4/3) is (-1/3). The slope of a perpendicular line is 3.
To find the x-intercept of y = (-2/5)x + 4, plug in 0 for y and find x.
0 = (-2/5)x + 4
x = 10
The equation of the line right now is y = 3x + b
Plug in (10, 0) to find the y-intercept.
0 = 3(10) + b
b = -30
The equation of the line is y = 3x - 30