Problem 21 · 2020 Math Kangaroo
Stretch
Algebra & Patterns
evaluate-formula
The figure shows the lines r and s, whose equations are \(y = ax + b\) and \(y = cx + d\) respectively. Which of the following statements is true?
Show answer
Answer: A — \(ab + cd < 0\)
Show hints
Hint 1 of 2
Read the signs: r is (nearly) horizontal and high up; s rises steeply through the lower region.
Still stuck? Show hint 2 →
Hint 2 of 2
Get the sign of each of a, b, c, d, then test the options.
Show solution
Approach: read coefficient signs from the graph
- Line r is horizontal with positive intercept, so its slope a is 0 (or tiny) and b > 0.
- Line s has positive slope c > 0 and negative intercept d < 0.
- Then ab is about 0 and cd < 0, so ab + cd < 0 always holds: option A.
Mark:
· log in to save