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.
Alaska 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
Lines & Intersections in Alaska
In the Alaska content 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: Alaska Department of Education and Early Development
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
Plan A is y = 5x + 50 and Plan B is y = 10x + 20, where x is months and y is total cost in dollars. The lines meet at (6, 80). What does this point mean?
- Plan A costs $6 and Plan B costs $80
- Both plans cost $80 per month
- After 80 months both plans cost $6
- After 6 months both plans cost $80
After 6 months both plans cost $80
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 2
The line y = 4x is translated 3 units to the right. What is its new equation?
- y = 4x + 3
- y = 4x + 12
- y = 4x − 3
- y = 4x − 12
y = 4x − 12
Hint: Every point moves 3 to the right: replace x with (x − 3), so y = 4(x − 3).
Question 3
Which point is in the region y > x + 1?
- (4, 5)
- (1, −1)
- (−1, 4)
- (−3, −5)
(−1, 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.
Question 4
What is the x-intercept of the line 3x + 2y = 6?
answer box
2
Hint: On the x-axis y = 0, so 3x = 6 and x = 2.
Question 5
The line y = 4x is rotated 90° about the origin. What is the equation of the image?
- y = 4x
- y = −x/4
- y = x/4
- y = −4x
y = −x/4
Hint: After a quarter turn, the new slope is the negative reciprocal of the old slope.
Question 6
The lines y = −x + 9 and y = 3x − 3 meet at one point. What is the y-coordinate of that point?
answer box
6
Hint: Set the two expressions equal: −x + 9 = 3x − 3. Solve for x to get x = 3, then put x back to find y = 6.