write the slope-intercept form of an equation for a line that passes through A(3,4)and is perpendicular to the line that passes through e(4,1) and F(-2,4)

The line you want to be perpendicular to has slope (4-1)/(-2 -4) = -1/2

That means the line you want to draw has slope m = 2. (The product of the two slopes must be -1)

Your equation will be y = 2x + b, where
4 = 2*3 + b
b = -2

y = 2x - 2 is the equation.