Linear Relationships — O/L Mathematics

What must I remember about Linear Relationships?

• Standard equation of a straight line in the Cartesian coordinate plane is y = mx + c.
• Gradient (m) measures the slope of the line: m = (y₂ - y₁) / (x₂ - x₁) = (vertical change) / (horizontal change).
• Y-intercept (c) is the y-coordinate of the point where the line cuts the y-axis (coordinates (0, c)).
• Parallel lines property: Two distinct non-vertical lines are parallel if and only if their gradients are equal: m₁ = m₂.
• Lines passing through the origin take the direct proportion form y = mx (c = 0).

Test yourself (1 minute)

1. Gradient subtraction order consistency

   In m = (y₂ - y₁) / (x₂ - x₁), maintain the same point order in numerator and denominator; mixing them flips the gradient sign.

2. Positive vs negative gradient

   A line sloping upwards from left to right has m > 0; a line sloping downwards has m < 0; horizontal line has m = 0; vertical line has undefined gradient.

3. Rearranging to standard form

   Before reading off m and c, always rearrange the equation into subject y form: from 2y - 4x = 6 to y = 2x + 3 (m = 2, c = 3).

Practise Linear Relationships questions today

Source: NIE G.C.E. (O/L) Mathematics Syllabus (Grade 10, Unit 20)

What should I study first?

Next in the syllabus

Where does Linear Relationships fit in the syllabus?

Grade 10 · Term 2