STRAIGHT LINES
Frequently Asked Questions
A straight line is the shortest path between two points and is represented by a linear equation in the coordinate plane.
The general form is \(Ax + By + C = 0\), where \(A, B\) are not both zero.
The slope is the measure of inclination and is given by \(m = \tan \theta\), where \(\theta\) is the angle with the positive \(x\)-axis.
For points \((x_1, y_1)\) and \((x_2, y_2)\), slope \(m = \frac{y_2 - y_1}{x_2 - x_1}\).
The slope-intercept form is \(y = mx + c\), where \(m\) is slope and \(c\) is the \(y\)-intercept.
The intercept form is \(\frac{x}{a} + \frac{y}{b} = 1\), where \(a\) and \(b\) are \(x\)- and \(y\)-intercepts.
The point-slope form is \(y - y_1 = m(x - x_1)\).
The two-point form is \(\frac{y - y_1}{y_2 - y_1} = \frac{x - x_1}{x_2 - x_1}\).
The normal form is \(x \cos \alpha + y \sin \alpha = p\).
Slope indicates the steepness and direction of a line.
A line is parallel to the \(x\)-axis if its slope \(m = 0\).
A line parallel to the \(y\)-axis has undefined slope.
The equation is \(y = k\), where \(k\) is a constant.
The equation is \(x = k\), where \(k\) is a constant.
Two lines are parallel if their slopes are equal, \(m_1 = m_2\).