write equation of the line with the given pt and parallel to the given line (8,9); x+5y=4

Question

I need help solving this I don't understand what they are asking me to do

Answer 1

First thing:  Parallel to the given line.  That means the slope of your line should be the same as the the slope of x + 5y = 4.  We need to find the slope of x + 5y = 4.

x + 5y = 4

5y = -x + 4

y = (-1/5)x + 4/5

The slope is -1/5

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Second thing:  Make the new line.  We know a point (8,9) and the slope (-1/5), so we can use point-slope form:

y - y1 = m(x - x1)

y - 9 = (-1/5)(x - 8)

That is the equation of our line, but let's clean it up a bit:

y - 9 = (-1/5)x + 8/5

y = (-1/5)x + 8/5 + 9

y = (-1/5)x + 8/5 + 45/5

y = (-1/5)x + 53/5

y + (1/5)x = 53/5

5y + x = 53

Answer:  x + 5y = 53

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Note:  Unless the problem specifically asks for a certain form (give the answer in whatever form), we want to give the answer in the form used in the problem.