9th grade · Math · Unit 8 of 17
Lines & Intersections
Graphs, inequalities and transformations
What your child practices
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.
Maine Learning Results learning standard: HSA.REI.D.11; HSF.BF.B.3 · where two graphs meet, and how a graph moves when its equation changes
How we explain it
Children can open this short lesson before they practice.
- A line y = mx + b has slope m and y-intercept b.
- Slope is rise ÷ run.
- To graph it, start at b on the y-axis, then use the slope.
Example: What is the slope of y = 3x − 2? Compare to y = mx + b. m = 3. Answer: 3
Lines & Intersections in Maine
In the Maine Learning Results, this is unit 8 of 17 in 9th grade Math, after Expressions and before Data & Scatter Plots.
Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.
Source: Maine Department of Education
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
Which point is in the region y < 2x?
- (1, 4)
- (3, 6)
- (2, 3)
- (−2, −1)
(2, 3)
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.
Question 2
What is the x-intercept of the line 5x + 6y = 60?
answer box
12
Hint: On the x-axis y = 0, so 5x = 60 and x = 12.
Question 3
Which describes the graph of x = 3?
- A vertical line through (3, 0)
- A vertical line through (0, 3)
- A horizontal line through (0, 3)
- A line through the origin with slope 3
A vertical line through (3, 0)
Hint: x = k means every point has the same x-value, so the line goes straight up and down through that x on the x-axis.
Question 4
Plan A costs $40 to join plus $10 per month. Plan B has no joining fee and costs $20 per month. After how many months do the two plans cost the same?
answer box
4
Hint: Total cost: A = 40 + 10m and B = 0 + 20m. Set them equal and solve for m.
Question 5
Plan A is y = 10x + 50 and Plan B is y = 20x + 20, where x is months and y is total cost in dollars. The lines meet at (3, 80). What does this point mean?
- After 80 months both plans cost $3
- Both plans cost $80 per month
- After 3 months both plans cost $80
- Plan A costs $3 and Plan B costs $80
After 3 months both plans cost $80
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 6
The line y = 5x is rotated 180° about the origin. What happens?
- y = −5x
- y = x/5
- y = 5x + 1
- It lands on itself: the same line
It lands on itself: the same line
Hint: A half turn about the origin sends each point (x, y) to (−x, −y), which is on the same line through the origin.