To start, first convert 7x-2y=3 from standard form to slope intercept form. To do this, first subtract over 7x to get -2y=-7x+3. Then, divide both sides by -2 to get
y=7/2x-3/2
Now that you have this in slope intercept form, take the m value of the equation, 7/2 and find the negative reciprocal of it. This will be the value of the slope of a line perpendicular to 7x-2y=3. Your final answer will be -2/7.