General Linear Equation, Parallel and Perpendicular Lines, and the Angle Between Lines

In the equation \(Ax+By+C=0\), if \(B=0\) (but \(A\neq 0\)), the line represented is:

In the equation \(Ax+By+C=0\), if \(A=0\) (but \(B\neq 0\)), the line represented is:

For the line \(Ax+By+C=0\) (with \(B\neq 0\)), the slope of the line is given by:

A line parallel to 3x − 5y = 11

Find the equation of the line through (6, 8) that is parallel to the line 3x − 5y = 11. Give the equation in the form 3x − 5y + k = 0 (find k).

A line parallel to 3x − 5y = 11

Find the equation of the line through (6, 8) that is parallel to the line 3x − 5y = 11. Give the equation in the form 3x − 5y + k = 0 (find k).

Two perpendicular lines l₁ and l₂

Two nonvertical lines with slopes m1 and m2 are perpendicular to one another if and only if:

The tangent of the angle \(\theta\) from line \(l_1\) (slope \(m_1\)) to line \(l_2\) (slope \(m_2\)) is given by:

Find \(\tan\theta\), the tangent of the angle from \(l_1: y - 2x = 2\) to \(l_2: 2y + 5x = 17\). Express your answer as a fraction.

Find \(\tan\theta\), the tangent of the angle from \(l_1: y - 2x = 2\) to \(l_2: 2y + 5x = 17\). Express your answer as a fraction.