Resources / Functions

📍 Line through two points

Two points give the slope and, from it, the equation of the line. Then it is checked against the other point.

Point A

(,)

Point B

(,)
Examples:
y = 2x + 2
xy−4−3−2−1123456−6−4−22468101214Point A (0, 2)(0, 2)Point B (3, 8)(3, 8)X-axis crossing (−1, 0)(−1, 0)

Points

  • Point A:(0, 2)
  • Point B:(3, 8)
  • X-axis crossing:(−1, 0)

Slope (m)

2

Y-intercept (b)

2

Behaviour

Increasing

Equation of the line

  1. The slope is the rise in y divided by the run in x:
  2. m = (y₂ − y₁) / (x₂ − x₁) = (8 − 2) / (3 − 0) = 6 / 3 = 2
  3. Substitute point A into y = mx + b to find b:
  4. 2 = 2·0 + b → b = 2 − 0 = 2
  5. The line is y = 2x + 2
  6. Check with B: 2·3 + 2 = 8 ✓

Where it crosses the Y axis

  1. On the Y axis, x is 0. Substitute:
  2. y = f(0) = 2 → (0, 2)

Where it crosses the X axis

  1. On the X axis, y is 0. Solve:
  2. 2x + 2 = 0
  3. 2x = −2
  4. x = −2 / 2 = −1

Practise functions

📈 Function Hunt📝 Functions exam📝 Lines exam🖨️ More resources
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