Parallel lines：練習問題

In the diagram, line \(AB\) is parallel to line \(CD\). If an alternate interior angle formed by a transversal is \(62^\circ\), what is the size of its corresponding alternate interior angle?

A line \(K\) passes through the points \((1, 2)\) and \((3, 8)\). Line \(M\) is parallel to line \(K\). What is the gradient of line \(M\)?

Line \(L_1\) has the equation \(4x + ky = 12\). Line \(L_2\) is parallel to \(L_1\) and passes through the points \((0, 2)\) and \((2, 1)\). Find the value of the constant \(k\).

Line L has the equation \(y = 5x - 2\). What is the gradient of any line that is parallel to line L?

Find the y-intercept of the line that is parallel to \(y = -2x + 7\) and passes through the point \((4, 3)\).

The line \(L_1\) has the equation \(y = 2x - 5\).
Find the equation of the line \(L_2\) which is parallel to \(L_1\) and passes through the point \((3, 4)\).
Give your answer in the form \(y = mx + c\).

Find the equation of the line that is parallel to \(2y = 6x - 10\) and passes through the point \((0, 7)\). Give your answer in the form \(y = mx + c\).

A line \(L_1\) has the equation \(y = 4x - 2\).
(a) Write down the gradient of any line parallel to \(L_1\).
(b) Find the equation of the line \(L_2\) that is parallel to \(L_1\) and passes through the point \((1, 6)\).
(c) Find the y-intercept of the line \(L_2\).

Line \(L_1\) passes through the point \((0, 4)\) and has a gradient of 2.
(a) Write down the equation of line \(L_1\).
(b) Find the equation of line \(L_2\) which is parallel to \(L_1\) and passes through the point \((2, 0)\).
(c) Point P lies on line \(L_2\) and is at a distance of \(\sqrt{20}\) from the origin \((0, 0)\). Find the coordinates of the two possible positions of P.