Math 1050 slope question

Question

Find an equation of a line that passes through the point (-A, B-3) and is perpendicular to the line Ax+By=C.

Answer 1

Ax + By = C

 

Let's put that equation into the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.

 

Ax + By = C

By = -Ax + C

y = (-A/B)x + (C/B)

 

The slope of this line, then, is m = -A/B.  The slope of the line we are looking for is perpendicular to this line, which means its slope is the negative inverse (-1/m); so the slope of the line we want is B/A.  The line's equation so far is:

 

y = (B/A)x + b

 

To find b, plug in the values of the known point given in the problem statement: (-A,B-3)

 

B-3 = (B/A)*(-A) + b

B-3 = -B + b

2B-3 = b

 

The final equation, then, is:

 

y = (B/A)x + (2B-3)