Question

Find an equation of the line perpendicular to the graph of 10x - 5y = 8 that passes through the point at (-4, 7)

Answer 1

We need to swap the numerator and denominator, and change the sign of one of them to get a perpendicular slope.5x + 10y = c. Now subtract the point.
5(-4) + 10(7) = -20 + 70 = 50 = c 
5x + 10y = 50 is an equation. If we want, we can divide everything by 5 to get x + 2y = 10.The more usual way to do these is put the equation in slope-intercept form by solving for y. 10x-5y=8 -5y = -10x + 8 y = 2x - 8/5 Now you have the slope of the original line, 2. Any line perpendicular to this one must have a slope that is the negative reciprocal of this one, -1/2 So this new line must be y = -1/2 x + c .Now subtract in point to solve for c.
7 = (-1/2)(-4) + c 7 = 2+c 
5 = c 
y = -1/2 x + 5 
The first time we solved we got this. 
x + 2y = 10 but, if we divide everything by 2, we get 1/2 x + y = 5 So... subtract 1/2 x from both sides and you have identical equations. So the two are equivalent. The answer is y = -1/2 x + 5 
Hope this helped!