Question

The equation of the line passing through the point \((-9,5)\) and parallel to the line \(5x - 13y = 19\) is:

• A. \(5x - 13y + 110 = 0\)
• B. \(5x - 13y + 100 = 0\)
• C. \(5x - 13y + 65 = 0\)
• D. \(5x - 13y - 110 = 0\)
• E. \(5x - 13y - 100 = 0\)

Hint:

When determining the equation of a line parallel to another, maintain the same coefficients for \(x\) and \(y\) to ensure the slope remains constant, then solve for the constant term using a given point.

Answer 1

The Correct Option is A

To find the equation of a line parallel to \(5x - 13y = 19\) and passing through the point \((-9, 5)\), we use the fact that parallel lines have the same slope, hence the same coefficients for \(x\) and \(y\).
The general form of the line is: \[ 5x - 13y + C = 0 \] Substituting the point \((-9, 5)\) into the equation to find \(C\): \[ 5(-9) - 13(5) + C = 0 \] \[ -45 - 65 + C = 0 \] \[ C = 110 \] Thus, the equation of the line is: \[ 5x - 13y + 110 = 0 \]