Secondary 3 G2 Mathematics Tutor Bukit Timah | Gradient of Parallel and Perpendicular Lines. Did you know? Two lines can have equal gradients without ever meeting.
This quick-reference guide explains gradient of parallel and perpendicular lines for Secondary 3 G2 Mathematics students in Bukit Timah, with worked examples, mistakes to avoid and independent practice.
What does gradient measure?
Gradient is vertical change divided by horizontal change. Between (1,2) and (5,10), the gradient is (10−2)/(5−1)=2. It measures two units of rise for every one unit across.
Try explaining this step in your own words before checking a second example. A useful Mathematics tutorial checks the first incorrect decision, then changes the numbers or diagram to test whether the method transfers.
Parallel lines
Distinct nonvertical parallel lines have equal gradients. y=2x+1 and y=2x−4 both have gradient 2 but different intercepts, so they never intersect.
Try explaining this step in your own words before checking a second example. A useful Mathematics tutorial checks the first incorrect decision, then changes the numbers or diagram to test whether the method transfers.
Perpendicular lines
For nonvertical perpendicular lines, gradients multiply to −1. A line with gradient 2 is perpendicular to one with gradient −1/2. Horizontal and vertical lines are a special perpendicular pair.
Try explaining this step in your own words before checking a second example. A useful Mathematics tutorial checks the first incorrect decision, then changes the numbers or diagram to test whether the method transfers.
Find an equation
Through (3,4) with gradient 2, y−4=2(x−3), hence y=2x−2. Substituting (3,4) verifies the equation.
Try explaining this step in your own words before checking a second example. A useful Mathematics tutorial checks the first incorrect decision, then changes the numbers or diagram to test whether the method transfers.
Common mistake
Do not confuse a y-intercept with gradient. In y=3x+7, gradient is 3 and intercept is 7. The signs matter.
Try explaining this step in your own words before checking a second example. A useful Mathematics tutorial checks the first incorrect decision, then changes the numbers or diagram to test whether the method transfers.
Self-check
Find the gradient through (2,5) and (6,13): (13−5)/(6−2)=2. A parallel line has gradient 2; a nonvertical perpendicular line has gradient −1/2.
Try explaining this step in your own words before checking a second example. A useful Mathematics tutorial checks the first incorrect decision, then changes the numbers or diagram to test whether the method transfers.
Frequently asked questions
What should I do first? Identify the given values and the quantity required. How can I check the result? Substitute it into the original information and verify the units or graph. Why might a correct-looking answer fail? A sign, denominator or interpretation error can change the meaning of the result.
Official syllabus and tutorial context
Consult the 2027 SEC G2 Mathematics K210 syllabus for the official topic and assessment scope. The unchanged eduKateSG three-pupil Mathematics reference describes small-group teaching near Sixth Avenue. Confirm current Secondary 3 G2 tutor, fees, venue, group fit and timetable directly.
Continue the Secondary 3 G2 Bukit Timah series
For further Mathematics revision, see factorisation by grouping, quadratic graphs, and critical reading of data.