Question

What is the slope of the line with the equation of y=-4x that passes through the point (3,1)

Answer 1

The question seems incomplete but that could just be my perception.

The slope of y = -4x is -4 as it's the value just in front of the x value. This equation is in the form y = mx+b where m = -4 and b = 0. The m is the slope.

Anything parallel to y = -4x will also have a slope of -4. Parallel lines have equal slopes (but different y intercepts)

Anything perpendicular to y = -4x will have a slope of 1/4. Notice how multiplying the original slope (-4) and the perpendicular slope (1/4) gets you -1. To go from -4 to 1/4, we flip the fraction and the sign. Think of -4 as -4/1 to flip the fraction to -1/4 and then flip the sign to +1/4 or just 1/4.