A point and a slope determines the equation of a line. Since x intercept is 4, the point is (4,0) because x intercept is the value of x if y=0. To find the slope, first find the slope of 4x-y-3=0. Isolating y, y=4x-3. Since y=mx+b, m=4. But we are finding the perpendicular line, so it is negative reciprocal of m, which is -1/4. y-0=(-1/4)(x-4). y=-(1/4) (x-4)