9th grade · Math · Unit 3 of 18
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.
Alabama Course of Study content standard: GDA.3; GDA.5 · where two lines meet, and the graph of a linear equation as the set of its solutions
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 Alabama
In the Alabama Course of Study, this is unit 3 of 18 in 9th grade Math, after Rearranging Formulas and before Linear Relations.
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 lines y = −4x + 19 and y = −x + 7 meet at one point. What is the y-coordinate of that point?
answer box
3
Hint: Set the two expressions equal: −4x + 19 = −x + 7. Solve for x to get x = 4, then put x back to find y = 3.
Question 2
Plan A is y = 10x + 70 and Plan B is y = 20x + 20, where x is months and y is total cost in dollars. The lines meet at (5, 120). What does this point mean?
- After 5 months both plans cost $120
- Both plans cost $120 per month
- After 120 months both plans cost $5
- Plan A costs $5 and Plan B costs $120
After 5 months both plans cost $120
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
What is the y-intercept of the line 6x + 3y = 18?
answer box
6
Hint: On the y-axis x = 0, so 3y = 18 and y = 6.
Question 4
Which point is in the region y > 2x + 5?
- (4, 14)
- (2, 9)
- (3, 10)
- (−3, −3)
(4, 14)
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
Which describes the graph of y = 2?
- A vertical line through (2, 0)
- A horizontal line through (0, 2)
- A horizontal line through (2, 0)
- A line through the origin with slope 2
A horizontal line through (0, 2)
Hint: y = k means every point has the same y-value, so the line runs flat across through that y on the y-axis.
Question 6
The line y = −3x is translated 2 units to the right. What is its new equation?
- y = −3x − 6
- y = −3x + 2
- y = −3x − 2
- y = −3x + 6
y = −3x + 6
Hint: Every point moves 2 to the right: replace x with (x − 2), so y = −3(x − 2).