Question

Write the equation of a line that is perpendicular to the given line and that passes through the given point.
y-2=7/3 (x+5);(-4,9)

You don't have to give me the answer, but steps or a walk through would be nice so i can do it on my own in the future

Answer 1

the slope of equation above is:
\(m=7/3\)
now, the slope \(m'\) of the requested line has to be:
\[\Large m' = \frac{{ - 1}}{m} = \frac{{ - 1}}{{\frac{7}{3}}} = ...?\]

Answer 2

the requested equation, is:
\[y - 9 = m'\left( {x + 4} \right)\]

Answer 3

is it y-9=-3/7 (x-4)?

Answer 4

sorry it took awhile my baby brother came in and started distracting me

Answer 5

no problem, here we have to apply this formula:
\[y - {y_0} = m'\left( {x - {x_0}} \right)\]
where \(x_0=-4\)

Answer 6

y−y0=m′(x−x0)

(-4,9)

m′=-3/7

applying these gets me

y-9=-3/7(x-4)
correct?
or is it y-9=-3/7(x+4) because you would be subtracting a negative

Answer 7

@Michele_Laino

Answer 8

it is the second equation, namely:
\[y - 9 = \frac{{ - 3}}{7} \cdot \left( {x + 4} \right)\]

Answer 9

Okay thanks!!! i just wanted to verify so i understand everything.

Answer 10

:)