The general equation of a straight line in the plane can be written as \(ax+by+c=0\), where \(a\) and \(b\) are not both zero.

The slope of the line parallel to the \(x\)-axis is zero.

The slope of the line perpendicular to the \(x\)-axis is zero.

If the slope of a line is positive, the line rises from left to right.

The equation \(y=3\) represents a line parallel to the \(y\)-axis.

The slope–intercept form of a straight line is \(y=mx+c\).

The equation \(x=5\) represents a vertical line.

Two lines having equal slopes are always coincident.

The point \((0,0)\) lies on the line \(y=mx\) for all real values of \(m\).

The intercept form of a line is \(\frac{x}{a}+\frac{y}{b}=1\).

The slope of the line joining the points \((x_1,y_1)\) and \((x_2,y_2)\) is \(\frac{y_2-y_1}{x_2-x_1}\), provided \(x_1\neq x_2\).

The angle between a line of slope \(m\) and the positive \(x\)-axis is given by \(\tan^{-1}m\).

If two lines are perpendicular, the product of their slopes is 1.

The equation of a line passing through \((x_1,y_1)\) with slope \(m\) is \(y-y_1=m(x-x_1)\).

The distance between the parallel lines \(ax+by+c_1=0\) and \(ax+by+c_2=0\) is \(\frac{|c_1-c_2|}{\sqrt{a^2+b^2}}\).

All lines of the form \(y=mx+c\) pass through the origin.

The condition for three points \((x_1,y_1)\), \((x_2,y_2)\), and \((x_3,y_3)\) to be collinear is \(\begin{vmatrix}x_1&y_1&1\\x_2&y_2&1\\x_3&y_3&1\end{vmatrix}=0\).

If the slopes of two lines are \(m_1\) and \(m_2\), then the tangent of the angle between them is \(\left|\frac{m_2-m_1}{1+m_1m_2}\right|\).

The line \(ax+by+c=0\) cuts equal intercepts on the axes if and only if \(a=b\).

The family of lines \(y=mx+1\) for different values of \(m\) all pass through a fixed point.

The angle between the lines \(y=mx\) and \(y=-\frac{1}{m}x\) is \(90^\circ\) for all non-zero \(m\).

The equation of the line perpendicular to \(ax+by+c=0\) has slope \(\frac{b}{a}\).

If a line has infinite slope, it is parallel to the \(y\)-axis.

The locus of a point moving such that its distances from the \(x\)-axis and \(y\)-axis are equal is the line \(y=x\).

The angle between the lines \(ax+by=0\) and \(bx-ay=0\) is always \(90^\circ\).