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.
Minnesota K-12 Academic Standards benchmark: 9.3.7.3; 9.3.7.1 · how a graph moves when its equation changes, and where two graphs 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 Minnesota
In the Minnesota K-12 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.
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 3 units to the right. What is its new equation?
- y = −4x + 12
- y = −4x − 12
- y = −4x + 3
- y = −4x − 3
y = −4x + 12
Hint: Every point moves 3 to the right: replace x with (x − 3), so y = −4(x − 3).
Question 2
Which point is in the region y < 3x − 5?
- (−1, −5)
- (1, 0)
- (4, 7)
- (−3, −16)
(−3, −16)
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 3
What is the x-intercept of the line 4x + 6y = 36?
answer box
9
Hint: On the x-axis y = 0, so 4x = 36 and x = 9.
Question 4
Plan A is y = 10x + 100 and Plan B is y = 20x + 20, where x is months and y is total cost in dollars. The lines meet at (8, 180). What does this point mean?
- Plan A costs $8 and Plan B costs $180
- Both plans cost $180 per month
- After 8 months both plans cost $180
- After 180 months both plans cost $8
After 8 months both plans cost $180
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 5
The lines y = 3x and y = 2x − 2 meet at one point. What is the y-coordinate of that point?
answer box
-6
Hint: Set the two expressions equal: 3x = 2x − 2. Solve for x to get x = −2, then put x back to find y = −6.
Question 6
Plan A costs $40 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
3
Hint: Total cost: A = 40 + 10m and B = 10 + 20m. Set them equal and solve for m.