Advanced Algebra · 1.07/Overview
Advanced Algebra · Activity 1.07
See the algebra.
Move the math.
An interactive companion for the 1.07 Bonus Activity. See every linear–quadratic system, compare graphing with substitution, and decode the final riddle.
INTERSECTIONS2 solutions
✦Graph = story
9activity questions
6guided graph stops
2methods compared
1ridiculous duck joke
Start here
Learn the methods
Before solving the bonus, learn how to construct each graph and what to do at every substitution step.
GRAPHING A LINE
Turn y = mx + b into two points.
y = 2x − 3
Step 1 of 4
Start at the y-intercept: (0, −3).
Featured activity
1.07 Bonus Lab
Every problem from the bonus activity, rebuilt as an explorable demonstration.
0/6explored
LIVE GRAPH
Graph 1 · Two intersections
ACTIVITY MAP
Choose a stop
01
YOUR TURN · QUESTION 1 OF 2
How many solutions does this graph show?
A solution is a point that lies on both graphs.
AFTER YOU ANSWER
The worked explanation is locked
BONUS PAYOFF
Decode the duck joke
Explore all six stops to reveal the answer letters.
1.07 free practice
Practice Studio
Change the equations, predict before looking, and use the graph to test your reasoning.
Shape the equations
YOUR SYSTEM
2 solutions
Predict first:How many real solutions?
Construct
Line: plot b, then use rise/run. Parabola: plot the vertex, axis, and symmetric points.
Read
Every shared point is a solution. Record both coordinates, not only x.
Solve
Set the y-expressions equal, simplify, and solve the resulting quadratic.
Finish
Substitute each x back to find y, write ordered pairs, and check both equations.