MathematicsExam code: 0580
Linear Graphs
Coordinate Geometry and Graphs
Same gradient, different intercept
- Two different lines are parallel exactly when their gradients are equal (or both are vertical), and they then never meet
- y = 7x + 2 and y = 7x − 5 are parallel; y = 7x + 2 and y = 4x + 2 are not
- Check by rearranging both equations into y = mx + c first, since a shared gradient can be hidden by the form
- To find the equation of a line parallel to a given one, copy the gradient across and then find the new intercept from the point you are given
Worked example
Parallel through a given point
A line is parallel to y = 7x + 2 and passes through (3, 8). Find its equation.
Solution:
- Parallel means the same gradient, so the new line is y = 7x + c
- Substitute x = 3 and y = 8: 8 = 21 + c
- Subtract 21: c = −13
- The line is y = 7x − 13