Equation of Straight Lines
→ Slope = \frac{y_2−y_1}{x_2−x_1} = tan θ
→ Equation :
1. y − y_1 = m(x − x_1)
2. y = mx + c
3. \frac{x}{a} + \frac{y}{b} = 1 (🌟比較少用，可不記)
→ Parallel and Perpendicular
If L_1 // L_2, then m_1 = m_2
If L_1 ⊥ L_2, then m_1 × m_2 = −1
→ Distance between two points : \sqrt{(x_1 − x_2)^2 + (y_1 − y_2)^2}
→ Mid-point = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})
→ Section formula : C = (\frac{nx_1+mx_2}{m+n} , \frac{ny_1+my_2}{m+n} )
→ Intersection between two lines :
For y = m_1x + c_1 and y = m_2x + c_2
| Number of intersection | Condition |
| 1 | m_1 ≠ m_2 |
| 0 | m_1 = m_2 , c_1 ≠ c_2 |
| Infinite many | m_1 = m_2 , c_1 = c_2 |
→ Short Cut (記唔到可以唔記)
For Ax + By + C = 0
x-intercept = − \frac{C}{A} / Put y = 0
y-intercept = − \frac{C}{B} / Put x = 0
Slope = − \frac{A}{B} / Change to y = mx + c, m is the slope
直線方程公式
→ 斜率 = \frac{y_2−y_1}{x_2−x_1} = tan θ
→ 方程：
1. y − y_1 = m(x − x_1)
2. y = mx + c
3. \frac{x}{a} + \frac{y}{b} = 1 (🌟比較少用，可不記)
→ 平行及垂直
若 L_1 // L_2 , 則 m_1 = m_2
若 L_1 ⊥ L_2 , 則 m_1 × m_2 = −1
→ 兩點距離：\sqrt{(x_1 − x_2)^2 + (y_1 − y_2)^2}
→ 中點 = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})
→ 截點公式：C = (\frac{nx_1+mx_2}{m+n} , \frac{ny_1+my_2}{m+n})
→ 兩線之間的交點：
對於 y = m_1x + c_1 及 y = m_2x + c_2
| 相交點數量 | 條件 |
| 1 | m_1 ≠ m_2 |
| 0 | m_1 = m_2 , c_1 ≠ c_2 |
| 無限 | m_1 = m_2 , c_1 = c_2 |
→ Short Cut (記唔到可以唔記）
對於 Ax + By + C = 0
x截距 = − \frac{C}{A} / Put y = 0
y截距 = − \frac{C}{B} / Put x = 0
斜率 = − \frac{A}{B} / 轉為 y = mx + c , m 為斜率
