9th grade · Math · Unit 8 of 22
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.
New York State Learning Standards learning standard: AI-A.REI.11; AI-F.BF.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 New York
In the New York State Learning Standards, this is unit 8 of 22 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.
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 line y = −4x is translated 2 units to the right. What is its new equation?
- y = −4x + 8
- y = −4x + 2
- y = −4x − 2
- y = −4x − 8
y = −4x + 8
Hint: Every point moves 2 to the right: replace x with (x − 2), so y = −4(x − 2).
Question 2
The line y = 4x is rotated 90° about the origin. What is the equation of the image?
- y = x/4
- y = −x/4
- y = 4x
- y = −4x
y = −x/4
Hint: After a quarter turn, the new slope is the negative reciprocal of the old slope.
Question 3
Plan A is y = 5x + 55 and Plan B is y = 10x + 20, where x is months and y is total cost in dollars. The lines meet at (7, 90). What does this point mean?
- After 7 months both plans cost $90
- Plan A costs $7 and Plan B costs $90
- Both plans cost $90 per month
- After 90 months both plans cost $7
After 7 months both plans cost $90
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 4
Which describes the graph of x = −4?
- A vertical line through (0, −4)
- A horizontal line through (0, −4)
- A vertical line through (−4, 0)
- A line through the origin with slope −4
A vertical line through (−4, 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 5
Plan A costs $30 to join plus $10 per month. Plan B costs $10 to join plus $20 per month. After how many months do the two plans cost the same?
answer box
2
Hint: Total cost: A = 30 + 10m and B = 10 + 20m. Set them equal and solve for m.
Question 6
What is the x-intercept of the line 3x + 5y = 30?
answer box
10
Hint: On the x-axis y = 0, so 3x = 30 and x = 10.