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Find the equation for the line that passes through the point (4,−4) , and that is parallel to the line with the equation y−1=−12(x+5) .

User LarsTech
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1 Answer

4 votes

Answer:

y + 4 = -12(x - 4)

Explanation:

Relationship between the slopes of parallel lines and finding the slope of the other line:

  • The slopes of parallel lines are the same, meaning finding the slope of y - 1 = -12(x + 5) will allow us to find the slope of the other line.

y - 1 = -12(x +5) is in the point-slope form of a line, whose general equation is given by:

y - y1 = m(x - x1), where

  • (x1, y1) is any point on the line,
  • and m is the slope.

Thus, the slope of both the other line and y - y1 = -12(x + 5) is -12.

Writing the equation of the other line:

  • We know that the slope of the other line is -12 and that it passes through the point (4, -4).

Now we can find the equation of the other line in point-slope form by substituting -12 for m and (4, -4) for (x1, y1):

y - (-4) = -12(x - 4)

y + 4 = -12(x - 4)

Therefore, y + 4 = -12(x - 4) is the equation of the line (in point-slope form) that passes through the point (4, -4) and it parallel to the line with the equation y - 1 = -12(x + 5).

User Ackerchez
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