Question

What is the equation of the line that is perpendicular to the line y=1/2x+7 and passes through the point (6,2)

Answer 1

y=1/2x+7, slope is 1/2
perpendicular so slope is opposite and reciprocal
slope = -2
passes through the point (6,2)
y - 2 = -2(x - 6)
y - 2 = -2x + 12
y = -2x + 14

answer
equation y = -2x + 14

Answer 2

Perpendicular lines have slopes that equal $-1$ when they are multiplied. To find the perpendicular slope, set up this equation (let $x$ represent the second equation):

$\frac{1}{2} (x)=-1$

So, $x=-2$.

Now, plug in the ordered pair given, $(6,2)$ into the equation $y=-2x+b$ and solve for $b$.

$2=6(-2)+b$

multiply

$2=-12+b$

add $12$ to both sides

$b=14$

insert the value of $b$ into the equation $y=-2x+b$

Answer: $y=-2x+14$

Hope this helps!