The required line is perpendicular to the line x - 4y = 2. This is the case when the product of the slope of the line and that of x - 4y = 2 is equal to -1.
x - 4y = 2 can be written as y = x/4 - 2/4 in slope intercept form. The slope of the required line is -4.
As it has the point (5, 2) its equation is:
(y - 2)/(x - 5) = -4
=> y - 2 = -4x + 20
=> y = -4x + 22
The equation of the required line in slope-intercept form is y = -4x + 22
Perpendicular to the line x - 4y = 2 containing the point (5,2)
Lets take your standard form equation and change it to slope-intercept to readily identify the slope:
4y = x - 2
y = (1/4)x - (1/2)
The slope is 1/4.
A perpendicular line's slope will be the negative reciprocal of this one so -4.
Now we have a point and a slope, lets first write out the perpendicular line in point-slope form.
y - 2 = -4(x - 5)
Distribute the -4 and solve for y to put this into slope-intercept form.
the slope of reqd line will be -4. and contains the pt (5,2)
(y-2)= -4(x- 5)
y+4x=22 divide by 22
y/22 + x/5.5= 1