Grade 9 · Math · Unit 11 of 15
Lines & Intersections
Graphs, inequalities and transformations
What your child practises
Finding where two lines meet and what it means in a story, graphing x = k, y = k and ax + by = k, regions of an inequality, and translating, reflecting and rotating lines through the origin.
Ontario Curriculum expectation: C3.3, C4.2, C4.3 · comparing linear relations, graphing equations and inequalities, and transforming lines
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
The lines y = 2x + 8 and y = x + 6 meet at one point. What is the x-coordinate of that point?
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-2
Hint: Set the two expressions equal: 2x + 8 = x + 6. Solve for x to get x = −2, then put x back to find y = 4.
Question 2
The line y = 4x is reflected in the y-axis. What is the equation of the image?
- y = −4x
- y = x/4
- y = −x/4
- y = 4x
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y = −4x
Hint: A reflection in either axis flips the sign of the slope but the line still passes through the origin.
Question 3
What is the x-intercept of the line 2x + 3y = 18?
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9
Hint: On the x-axis y = 0, so 2x = 18 and x = 9.
Question 4
Plan A is y = 10x + 35 and Plan B is y = 15x, where x is months and y is total cost in dollars. The lines meet at (7, 105). What does this point mean?
- Plan A costs $7 and Plan B costs $105
- After 7 months both plans cost $105
- Both plans cost $105 per month
- After 105 months both plans cost $7
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After 7 months both plans cost $105
Hint: The first number in a point is x (months) and the second is y (total cost). A point where the lines meet is where both plans cost the same.
Question 5
Plan A costs $10 to join plus $5 per month. Plan B has no joining fee and costs $10 per month. After how many months do the two plans cost the same?
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2
Hint: Total cost: A = 10 + 5m and B = 0 + 10m. Set them equal and solve for m.
Question 6
Which point is in the region y < −x + 1?
- (0, 4)
- (2, −4)
- (−3, 8)
- (3, −2)
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(2, −4)
Hint: Put each point into the inequality. A point on the line is not included because the sign is strict, and the other side of the line is the wrong region.