Formula Sheet

Straight Lines Formulas

All key formulas grouped by subtopic. Each one has a quick reminder and common mistakes to watch for.

8 formulas · 8 subtopics

y = mx + c

💡 m = slope, c = y-intercept. Slope = tan(θ) where θ is angle with positive x-axis.

m = \frac{y_2 - y_1}{x_2 - x_1}, \quad \frac{y - y_1}{y_2 - y_1} = \frac{x - x_1}{x_2 - x_1}

💡 Slope is undefined for vertical lines (x₁ = x₂).

d = \frac{|ax_1 + by_1 + c|}{\sqrt{a^2 + b^2}}

💡 Line: ax + by + c = 0. Don't forget the absolute value. Distance between parallel lines: |c₁-c₂|/√(a²+b²).

\tan\theta = \left|\frac{m_1 - m_2}{1 + m_1 m_2}\right|

💡 For perpendicular lines: m₁m₂ = -1. For parallel lines: m₁ = m₂.

⚠ Forgetting the absolute value gives the acute angle. Without |·| you get the signed angle.

L_1 + \lambda L_2 = 0

💡 Passes through the intersection of L₁ = 0 and L₂ = 0 for all values of λ. Choose λ to satisfy additional conditions.

\text{Area} = \frac{1}{2}|x_1(y_2-y_3) + x_2(y_3-y_1) + x_3(y_1-y_2)|

💡 Area = 0 means the points are collinear. Can also use determinant form.

\left(\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n}\right)

💡 Internal division: both +. External division: replace n with -n. Midpoint: m = n = 1.

\frac{x - x_1}{a} = \frac{y - y_1}{b} = -\frac{2(ax_1 + by_1 + c)}{a^2 + b^2}

💡 Line: ax + by + c = 0. The foot of perpendicular uses the same formula but with -1 instead of -2.