Year 9AC9M9A03
Summary of important concepts
Gradients — Determining the Gradient from Another Line
Find the gradient of a line segment, the midpoint of the line interval and the distance between 2 distinct points on the Cartesian plane.
Worked example
e.g. determine the gradient of the line perpendicular to y=21x+3 - Calculate the gradient of line 1m1=21
- If you need parallel lines, the second line's gradient is the samem2=21
- If you need perpendicular lines, use m1×m2=−1m1×m2=−1
- Substitute and solve for m221×m2=−1 ∴ m2=−2
Practice
Determine the gradient of the line:
1
parallel to y=3x−1 2
perpendicular to y=3x−1 Answerm=−31 3
parallel to 2y=3+x Answerm=21 4
perpendicular to y=2x Answerm=−21 5
perpendicular to x=y+3 6
parallel to y−6=x−3 7
perpendicular to x+2y=5 8
parallel to 3y=6x−9 9
perpendicular to 4x+y=7 Answerm=41 10
parallel to y=−65x Answerm=−65