ha8lokdrowlin
Answered

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).

Verified Answer :

meerkat18

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.

carlosego

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.

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