Equations of linear graphs: แบบฝึกหัด

What is the gradient of the straight line with the equation \(2y - 6x = 10\)?

State the gradient and the \(y\)-intercept for the linear graph with the equation \(2y = 6x - 4\).

The point \((k, 10)\) lies on the line joining \((0, 4)\) and \((2, 7)\). Find the value of \(k\).

The line segment joining \(A(-1, 4)\) and \(B(5, 12)\) is the diameter of a circle. Find the equation of the line that passes through the center of this circle with a gradient of \(-2\).

A straight line passes through the point (4, 7) and has a gradient of 3.

(a) Find the equation of this line in the form \(y = mx + c\).
(b) State the coordinates of the point where this line crosses the \(y\)-axis.

A straight line \(L\) passes through the point \(P(3, 5)\) and has a gradient of \(-2\).
(a) Find the equation of the line \(L\) in the form \(y = mx + c\).
(b) Another line, \(K\), is parallel to \(L\) and passes through the origin. Write down the equation of line \(K\).
(c) Find the coordinates of the point where line \(L\) crosses the \(x\)-axis.