9th grade · Math · Unit 8 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.
California Content Standards learning standard: A-REI.11; 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
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 = 2x + 8 and y = x + 6 meet at one point. What is the x-coordinate of that point?
answer box
-2
Hint: Set the two expressions equal: 2x + 8 = x + 6. Solve for x to get x = −2, then put x back to find y = 4.
Question 2
The line y = 4x is reflected in the y-axis. What is the equation of the image?
- y = −4x
- y = x/4
- y = −x/4
- y = 4x
y = −4x
Hint: A reflection in either axis flips the sign of the slope but the line still passes through the origin.
Question 3
What is the x-intercept of the line 2x + 3y = 18?
answer box
9
Hint: On the x-axis y = 0, so 2x = 18 and x = 9.
Question 4
Plan A is y = 10x + 35 and Plan B is y = 15x, where x is months and y is total cost in dollars. The lines meet at (7, 105). What does this point mean?
- Plan A costs $7 and Plan B costs $105
- After 7 months both plans cost $105
- Both plans cost $105 per month
- After 105 months both plans cost $7
After 7 months both plans cost $105
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
Plan A costs $10 to join plus $5 per month. Plan B has no joining fee and costs $10 per month. After how many months do the two plans cost the same?
answer box
2
Hint: Total cost: A = 10 + 5m and B = 0 + 10m. Set them equal and solve for m.
Question 6
Which point is in the region y < −x + 1?
- (0, 4)
- (2, −4)
- (−3, 8)
- (3, −2)
(2, −4)
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.