Question

Can someone check

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Answer 1

Both answers are incorrect.

Answer 2

Do this one step at a time.
What is the slope of the given line?

Answer 3

Its 1/6

Answer 4

Correct.
What is the slope of a perpendicular to that line?

Answer 5

-1

Answer 6

?
You need the negative reciprocal of the slope.
That means, flip the fraction and change the sign of 1/6.

Answer 7

so -6 ?

Answer 8

Good.
Now write the point-slope equation.

Answer 9

y+9=-6(x-7) ?

Answer 10

Correct.
Before you had the equation of the parallel line. (Same slope)
You needed the equation of the perpendicular line. (Negative reciprocal slope)
Now it's correct.
Now write the standard form.

Answer 11

x-6y=5?

Answer 12

No.
Start with the point-slope form which you have correct.
You need to multiply out the right side by distributing the -6.

Answer 13

6x+y=33

Answer 14

Good, or if your instructor prefers,
6x + y - 33 = 0