Question

Write an equation in slope-intercept form for the line perpendicular to the given line that contains Q. Q(6,3);y=- 1/2 x+9

Answer 1

You need a line with this equation:

$y=mx+b$

Where m is the slope and b is the intercept.

We know that it has to be perpendicular to

$y=-\frac{1}{2}x+9$

Two lines are perpendicular if their slopes are the opposite and reciprocal of each other. Therefore we have that the slope m has to be 2. For now we have:

$y=2x+b$

To find the intercept we use the given point Q(6,3). If we replace these values into the equation above, we can clear b:

$3=2\cdot6+b$$b=3-2\cdot6=3-12=-9$

Now we have the full equation of the line:

$y=2x-9$