58 exam-style questions on Equations of straight lines; gradient; parallel/perpendicular — topic 2.1 of Functions in the IB Mathematics: Applications and Interpretation syllabus — with answers and explanations. Samples below; the full set is free with an account.
Determine the gradient of the line that is perpendicular to the line y = 2x + 5.
Answer: −1/2
Perpendicular gradients are negative reciprocals: the negative reciprocal of 2 is −1/2.
State the gradient of the line with equation 3x + 4y = 12.
Answer: −3/4
Rearranging to y = −(3/4)x + 3 shows the gradient is −3/4.
Determine the equation of the line with gradient 3 passing through the point (2, 1).
Answer: y = 3x − 5
Using y − 1 = 3(x − 2) gives y = 3x − 6 + 1 = 3x − 5.
Two lines have gradients m₁ = 4 and m₂ = −1/4. Determine the relationship between the lines.
Answer: Perpendicular
Since m₁ × m₂ = 4 × (−1/4) = −1, the lines are perpendicular.
Calculate the gradient of the line through the points (−2, 5) and (4, −7).
Answer: −2
Gradient = (−7 − 5)/(4 − (−2)) = −12/6 = −2.
Determine the equation of the line parallel to y = −2x + 1 that passes through (0, 6).
Answer: y = −2x + 6
Parallel lines share the gradient −2; the y-intercept (0, 6) gives y = −2x + 6.
That was 6 of 58 Equations of straight lines; gradient; parallel/perpendicular questions.
Practise all 58 freeFindAO2 · 2–6 marks
Obtain the answer and show the method; if the calculator does it, say what was entered.
DetermineAO2 · 2–6 marks
Obtain the only possible answer — by calculation, from the graph or by reasoning — and show how.
StateAO1 · 1–2 marks
One word or one short sentence. No explanation, no working: the mark is for the fact itself.
58 Equations of straight lines; gradient; parallel/perpendicular questions — free with an account. Spaced repetition, streaks and full exam simulations included.
Practise them freeThis platform is independently developed and is not endorsed by, affiliated with, or sponsored by the International Baccalaureate Organization. “International Baccalaureate” and “IB” are registered trademarks of the IBO.