Question 1198735
slope intercept of the straight line equation is y = mx + b
your equation is x - 4y = 3
add 4y to both sides of the equation and subtract 3 from both sides of the equation to get x - 3 = 4y
divide both sides of the equation by 4 to get x/4 - 3/4 = y
switch sides on the equation to get y = x/4 - 3/4
this is the same as y = 1/4 * x - 3/4
a line perpendicular to the line of this equation is has a slope that is a negative reciprocal of the line.
that would be a slope of -4
the line perpendicular to the given line is therefore y = -4 * x - 3/4
the more general form of that equation is y = -4 * x + b
to find the equation of that line that passes through the point (2,10), replace x with 2 and y with 10 to get 10 = -4 * 2 + b
simplify to get 10 = -8 + b
add 8 to both sides of that equation to get 18 = b
the equation of the line perpendicular to the given line and passing through the point (2,10) is y = -4 * x + 18
here's a graph of both lines.


<img src = "http://theo.x10hosting.com/2022/113003.jpg">


the red line is the original line.
the blue line is the line perpendicular to it.