9th grade · Math · Unit 3 of 16
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.
Texas Essential Knowledge and Skills (TEKS) teks student expectation: A.2(G); A.3(E); A.3(F) · horizontal lines, shifts of the graph of f(x) = x, and where two lines meet
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 Texas
In the Texas Essential Knowledge and Skills (TEKS), this is unit 3 of 16 in 9th grade Math, after Coordinate Geometry and before Function Notation.
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: Texas Education Agency (TEA)
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 = −2x is translated 5 units to the right. What is its new equation?
- y = −2x + 5
- y = −2x − 5
- y = −2x − 10
- y = −2x + 10
y = −2x + 10
Hint: Every point moves 5 to the right: replace x with (x − 5), so y = −2(x − 5).
Question 2
The lines y = 4x + 21 and y = −3x − 7 meet at one point. What is the x-coordinate of that point?
answer box
-4
Hint: Set the two expressions equal: 4x + 21 = −3x − 7. Solve for x to get x = −4, then put x back to find y = 5.
Question 3
Which point is in the region y > 3x − 4?
- (4, 8)
- (−2, −14)
- (2, 6)
- (3, 3)
(2, 6)
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 4
Plan A costs $20 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
2
Hint: Total cost: A = 20 + 10m and B = 0 + 20m. Set them equal and solve for m.
Question 5
Plan A is y = 5x + 20 and Plan B is y = 15x, where x is months and y is total cost in dollars. The lines meet at (2, 30). What does this point mean?
- After 30 months both plans cost $2
- Plan A costs $2 and Plan B costs $30
- After 2 months both plans cost $30
- Both plans cost $30 per month
After 2 months both plans cost $30
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
Which describes the graph of x = −4?
- A line through the origin with slope −4
- A horizontal line through (0, −4)
- A vertical line through (0, −4)
- A vertical line through (−4, 0)
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.