GCSE(H),

**Perpendicular** lines exist at right angles to each other.

Two perpendicular lines are shown on the graph below. The line of one graph is given by *y* = 2*x* + 2, and the other by *y* = -`frac(1)(2)`*x* + 3.

Lines are perpendicular if the gradients of the two lines multiplied together = -1.

1. What is the equation of the line that is perpendicular to *y* = 3*x* -3 that also passes through (0, 5)?

Answer: y = -`frac(1)(3)`*x* + 5

The gradient of the original line is 3. The gradient of the perpendicular line = - `frac(1)(3)` (reciprocal of the original gradient x -1).

The intercept of the line is given by the fact that it passes through (0, 5).

2. Find the equation of the line perpendicular to *y* = `frac(1)(2)`*x* - 3 that passes through (4, 4).

Answer: *y* = -2*x* + 12

The gradient of the second line is given by - 1 / `frac(1)(2)` = -2.

The lines passes through the point (4, 4): 4 = -2 x 4 + *c*, where c is the intercept = 12.

The equation of the line is *y* = -2*x* + 12.

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