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13 votes
13 votes
Find the equation of the line that

is perpendicular to y = –
-x and
contains the point (4,-8).
y=
x + [ ]

Find the equation of the line that is perpendicular to y = – -x and contains the point-example-1
User Max Schmitt
by
2.2k points

1 Answer

7 votes
7 votes

Answer:

y = 3x/2-14

Explanation:

We are given that the line is perpendicular to y = -2/3 and contains (4,-8).

Perpendicular Def.


\displaystyle \large{m_1m_2 = - 1}

Both slopes multiply each others equal to -1.

Finding another slope that is perpendicular to -2/3, substitite m1 = -2/3 in.


\displaystyle \large{ - (2)/(3) m_2 = - 1}

Multiply both sides by 3.


\displaystyle \large{ - (2)/(3) m_2( 3) = - 1(3)} \\ \displaystyle \large{ - 2 m_2= - 3} \\ \displaystyle \large{ m_2= (3)/(2) }

Therefore, another slope that is perpendicular to -2/3 is 3/2.

Then rewrite in slope-intercept form.

Slope-Intercept


\displaystyle \large{y = mx + b}

where m = slope and b = y-intercept; substitute m = 3/2 in.


\displaystyle \large{y = (3)/(2) x + b}

Since the line contains (4,-8), substitute x = 4 and y = -8 in and solve for b.


\displaystyle \large{ - 8 = (3)/(2) (4) + b} \\ \displaystyle \large{ - 8 = 3(2)+ b} \\ \displaystyle \large{ - 8 = 6 + b} \\ \displaystyle \large{ - 8 - 6 = b} \\ \displaystyle \large{ - 14 = b}

Therefore, b is -14; rewrite again in slope-intercept form.

Thus:-


\displaystyle \large{y = (3)/(2) x + b} \\ \displaystyle \large{y = (3)/(2) x - 14}

User Skomski
by
3.0k points