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.
Arizona Academic Standards learning standard: A1.A-REI.D.11; A1.F-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 Arizona
In the Arizona Academic Standards, 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: Arizona 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
What is the y-intercept of the line 2x + 6y = 18?
answer box
3
Hint: On the y-axis x = 0, so 6y = 18 and y = 3.
Question 2
Plan A is y = 5x + 70 and Plan B is y = 15x + 20, where x is months and y is total cost in dollars. The lines meet at (5, 95). What does this point mean?
- After 95 months both plans cost $5
- After 5 months both plans cost $95
- Plan A costs $5 and Plan B costs $95
- Both plans cost $95 per month
After 5 months both plans cost $95
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 3
Plan A costs $50 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
5
Hint: Total cost: A = 50 + 10m and B = 0 + 20m. Set them equal and solve for m.
Question 4
Which point is in the region y > 3x − 3?
- (−2, −7)
- (3, 2)
- (−1, −6)
- (1, −2)
(−2, −7)
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 5
The lines y = 2x + 3 and y = 4x + 3 meet at one point. What is the y-coordinate of that point?
answer box
3
Hint: Set the two expressions equal: 2x + 3 = 4x + 3. Solve for x to get x = 0, then put x back to find y = 3.
Question 6
Which describes the graph of x = 4?
- A horizontal line through (0, 4)
- A vertical 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.