Answer:
[tex]y=-\frac{5}{2}x+\frac{11}{4}[/tex]
Step-by-step explanation:
To find a line perpendicular to 2x - 5y = 20, we need to find the slope of the line. To get the slope, we can solve for y, and get the equation in the form of y=mx + b
So I will solve for y:
[tex]2x - 5y = 20\\\\-5y=-2x+20\\\\y=\frac{2}{5} x-4[/tex]
So we know the slope is 2/5
The slope of a perpendicular line is the oposite reciprocal of original line. So the oposite reciprocal of 2/5 is -5/2. That will be our new slope
Now that we know the slope we can use the point slope formula to find an equation, then solve for y.
y-y₁=m(x-x₁)
y-4 = -5/2(x+ 1/2))
y= -5/2x + 11/4
