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Write the equation of the line that goes through (9,-4) and is perpendicular to the line
y = -3x – 8

Sagot :

facundo3141592

Answer: y = (1/3)*x - 7

Step-by-step explanation:

When we have a line:

y = a*x + b

A perpendicular line to this one needs to have a slope s equal to:

s = -(1/a)

Then any line written as:

y = -(1/a)*x + c

is perpendicular to the lines of the form "y = a*x + b"

Then if we have the line:

y = -3*x - 8

The family of perpendicular lines to this one is:

y = -(1/-3)*x + c

y = (1/3)*x + c

where c can be any real number.

Now we also want that this line passes through the point (9, -4)

Then we need to replace x by 9, and y by -4

-4 = (1/3)*9 + c

Now we can solve this for c.

-4 = 9/3 + c

-4 = 3 + c

-4 - 3 = c

-7 = c

Then the line that is perpendicular to the line y = -3x – 8 and that goes through (9, -4) is:

y = (1/3)*x - 7

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