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 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.

Answer 2

The generic equation of the line is:

$y-yo = m (x-xo)$

Where,

(xo, yo): point where the line passes

m: slope of the line

We have the following equation:

$4x - 3y = -8$

Rewriting we have:

$3y = 4x + 8$

$y = (\frac{4}{3}) x + \frac{8}{3}$

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

We have then:

$m =-\frac{3}{4}$

The point where the line passes is:

$(xo, yo) = (3, -2)$

Substituting values we have:

$y + 2 = -\frac{3}{4} (x-3)$

Answer:

the line that is perpendicular is:

$y + 2= -\frac{3}{4}(x-3)$

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