Two points $(a, 0)$ and $(0, b)$ are joined by a straight line. Another point on this line is:

$A$ line passes through $(x_{1}, y_{1})$ and $(h, k)$. If the slope of the line is $m$,show that $k - y_{1} = m(h - x_{1})$.

The gradient of the line joining the points on the curve $y = x^2 + 2x$ whose abscissae are $1$ and $3$,is

The equation of the line whose slope is $3$ and which cuts off an intercept of $3$ from the positive $x$-axis is

The equation of the line making an angle of $135^\circ$ with the positive $x$-axis and having a $y$-intercept equal to $-2$ is:

The intercept form of the equation of the straight line passing through the point $(4, -3)$ and perpendicular to the line passing through the points $(1, 1)$ and $(2, 3)$ is