2.1 Equations of straight linesIB Maths: Analysis and Approaches SL: Flashcards

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Gradient–intercept form of a line?

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Gradient–intercept form of a line?: $y = mx + c$
Point–gradient form of a line?: $y - y_1 = m(x - x_1)$
General form of a line?: $ax + by + d = 0$
Gradient between $(x_1, y_1)$ and $(x_2, y_2)$ ?: $\frac{y_2 - y_1}{x_2 - x_1}$
Condition for parallel lines?: $m_1 = m_2$
Condition for perpendicular lines?: $m_1\times m_2 = -1$
Gradient of $2x + 5y - 10 = 0$ ?: $y = -\frac25x + 2$ , so $-\frac25$ .
Gradient perpendicular to $m = -\frac25$ ?: $\frac52$
$x$ -intercept of $y = 3x - 6$ ?: $(2, 0)$
A road rises 30 m over 600 m horizontally. Gradient as a percentage?: $\frac{30}{600} = 0.05 = 5\%$
Line through $(2, 3)$ with gradient 4?: $y - 3 = 4(x - 2)$ , i.e. $y = 4x - 5$ .
How do you check a point lies on a line?: Substitute its coordinates; they must satisfy the equation.
Shortest distance from a point to a line is measured…: Along the perpendicular from the point to the line.