Question

Find the slope of a line perpendicular to the line ax + by=c

Answer 1

To find the slope of a line that is perpendicular to a given line, we can use the negative reciprocal of the slope of the given line.

The slope of a line in the form of ax + by = c is the coefficient of x (a) divided by the coefficient of y (b). In this case, the slope of the line is -a/b.

A line perpendicular to the line ax + by = c will have a slope that is the negative reciprocal of -a/b. So the slope of a line perpendicular to the line ax + by = c is b/a.

Note that when a = 0 or b = 0, the slope is undefined. In this case, the line is a vertical or horizontal line respectively and its perpendicular line is the other type of line.

Therefore, the slope of a line perpendicular to the line ax + by = c is b/a, as long as a is not equal to zero.

Answer 2

b/a

Step-by-step explanation:

ax + by = c

In order to find the slope put the equation in slope-intercept form (y=mx+b):

Solve for y:

ax + by = c

by = c - ax ==> subtract ax on both sides

y = (c - ax) / b ==> divide both sides by b to isolate y

y = c/b - ax/b ==> distribution property

y = -ax/b + c/b ==> turn the equation into y=mx+b format

-ax/b ==> The slope is -a/b

Now that we found the slope of the original line, we need to find the slope of the line perpendicular to it.

Perpendicular lines have slopes that are opposite reciprocals:

An example of opposite reciprocals are -1/2 and 2:

Negate 2 to get -2

-2 = -2/1 ==> any number that is divided by 1 is itself

The reciprocal of -2/1 is -1/2

Hence, the opposite reciprocal of 2 is -1/2

Now apply this concept to the slope -a/b:

Negate -a/b to get -(-a/b) = a/b

The reciprocal of a/b is b/a

Hence, the slope of the perpendicular line is b/a.