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 = 7x + 4?
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 = -2x + 4. Give the equation of a line, parallel to the given equation, that passes through (0, 5)
Answer: y = -2x + 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 = 2x + 5