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Use the given conditions to write an equation for the line.

Passing through (-7,7) and parallel to the line whose equation is 6x-5y-3=0

The equation of the line is _

(Simplify your answer. Type an equation using x and y as the variables. Use integers or fractions for any numbers in the equation.)

User Tanzmaus
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To find the equation of a line parallel to another line, we need to use the fact that parallel lines have the same slope. The given line has the equation 6x - 5y - 3 = 0, which we can rearrange to solve for y:

6x - 5y - 3 = 0
-5y = -6x + 3
y = (6/5)x - 3/5

The slope of this line is 6/5, so any line parallel to it will also have a slope of 6/5. We can use the point-slope form of the equation of a line to write the equation of the line passing through (-7,7) with this slope:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the point (-7,7):

y - 7 = (6/5)(x - (-7))

Simplifying, we get:

y - 7 = (6/5)x + 42/5

y = (6/5)x + 42/5 + 7

y = (6/5)x + 77/5

Therefore, the equation of the line passing through (-7,7) and parallel to the line 6x - 5y - 3 = 0 is y = (6/5)x + 77/5.
User Koninos
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