Математика15 мин

Slope of the Line

Compute slopes, write line equations in three forms, and recognise parallel and perpendicular lines instantly.

Slope from two points

m = \dfrac{y_2 - y_1}{x_2 - x_1}

Rise over run.

y - y_1 = m(x - x_1) \quad (\text{point–slope})

y = mx + b \quad (\text{slope–intercept})

Ax + By = C \quad (\text{standard})

Parallel lines: same $m$ . Perpendicular lines: $m_1 \cdot m_2 = -1$ .

Find a perpendicular

Find the line through $(2, 5)$ perpendicular to $y = -\tfrac{1}{2}x + 3$ .

Жауап: $y = 2x + 1$