Question

Alejandro made an error in the steps below when determining the equation of the line that is perpendicular to the line 4x – 3y = –8 and passes through the point (3, –2).

Answer 1

The generic equation of the line is:

`image`

Where,

(xo, yo): point where the line passes

m: slope of the line

We have the following equation:

`image`

Rewriting we have:

`image`

`image`

Since the lines are perpendicular, then the slope of the line is the inverse reciprocal.

We have then:

`image`

The point where the line passes is:

`image`

Substituting values we have:

`image`

Answer:

the line that is perpendicular is:

`image`

Note: compare with Alejandro's steps, in order to find the error.

Answer 2

The slope of the line given its equation is calculated through, m = -A / B. The slope of the given line is 4/3. The line perpendicular to it has the slope of -3/4. The slope-point form of the equation is,
y - y1 = m(x - x1)
where m is the slope and x1 and y1 the abscissa and ordinate of the point, respectively.
Substituting the values above,
y --2 = (-3/4)(x - 3)

Simplifying the equation gives 3x + 4y = 1.