Parallel lines: แบบฝึกหัด

Find the equation of the line that is parallel to \(y = 5x + 2\) and passes through the point (0, -4).

The line passing through (k, 5) and (4, 11) is parallel to the line passing through (2, -1) and (5, 8). Find the value of \(k\).

Find the equation of a line that is parallel to \(y = 5x + 2\) and passes through the origin \((0, 0)\).

Find the equation of the line passing through \((2, -3)\) that is parallel to the line \(3x + y = 10\).

Find the equation of the line that is parallel to \(y = 3x - 5\) and passes through the point (2, 10). Give your answer in the form \(y = mx + c\).

Two lines are represented by the equations:
Line 1: \(y = 5x + 2\)
Line 2: \(y = kx - 8\)

(a) If Line 1 and Line 2 are parallel, state the value of \(k\).
(b) Find the equation of a third line that is parallel to Line 1 and passes through the point (0, -3).