GCSE(F), GCSE(H),

**Parallel** lines have the same gradient, or slope, but different intercept points on the *y*-axis.

A set of **collinear** points all exist on the same line.

1. Is the line defined by two points, (2, 6) and (4, 20), parallel to the line given by the equation *y* = 7*x* + 4?

Answer: Yes

The gradient of the line defined by the points is `frac("difference up")("difference along")` = `frac(20-6)(4-2)` = 7.

Both gradients are the same, so the lines are parallel.

2. A line is given by an equation *y* = -2*x* + 4. Give the equation of a line, parallel to the given equation, that passes through (0, 5)

Answer: *y* = -2*x* + 5

The gradient is the same in both equations. The intercept for the second line is at *y* = 5.

The equation of the line is *y* = 2*x* + 5

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