A perpendicular equation to another equation has a slope that is the negative reciprocal of the slope of the equation. The negative reciprocal of -1/4 is 4, so the slope of the new line is 4. Our equation so far is y=4x+b. Then, since we know that it goes through the point (-4,3), we can substitute their values into the equation. This gives us a value of b of 19. This gives us the equation y=4x+19.