y = -4x + 17
Step-by-step explanation:
1st equation: y= 1/4x + 3
Point (x, y) = (4,1)
For one equation of line to be perpendicular to the other, the slope of one will be the negative reciprocal of the other one.
Equation of line form: y= mx + c
y= 1/4x + 3
Slope of the first = 1/4
reciprocal of the slope = 4/1
negative reciprocal = -(4/1) = -4
This means the slope of the second line = -4
we insert the slope and the point given in the equation formula to get the intercept (c):
Point (x, y) = (4,1)
1 = -4(4) + c
1 = -16 + c
1 + 16 = c
c = 17
Equation y= mx + c becomes: y = -4x + 17
The equation perpendicular to the given line through the given point is y = -4x + 17