Question

find an equation in slope intercept form for the line though point P(-3,2) and perpendicular to the line containing the two points (2,3) and (1,-2)

Answer 1

y=-1/5 x +7/5

Explanation:

First lets find the slope of the line containing the points (2,3) and (1,-2) by using the equation for slopes m1 = (y2 - y1) / (x2 - x1),

Which results in m1=5

If two lines are perpendicular, then their slopes must satisfy the following condition

m1*m2=-1

So, our new line must have the following slope (m2): m2*m1=1, if m1=5, then m2=-1/5

The line passes through P(-3,2)

Remember that the equation for a line is given by the following:

y=mx+b

if we eval P inside that equation, with m=-1/5

we have b.

2=-1/5*-3 +b

b=2-3/5