Lee and Lucas are playing a computer game. Lee has 80 points and loses 12 points each round. Lucas has 20 points and earns 3 points each round.

Question

The relationships between rounds played, x, and points, y, for Lee and Lucas are graphed on the coordinate plane below. What is the point of intersection?
x
y
Lee
Lucas
0
1
2
3
4
5
6
7
8
9
10
0
8
16
24
32
40
48
56
64
72
80
Rounds
Points
The point of intersection is (
,
).
Good work!
Now that you have found the point of intersection, (4, 32), let’s check that work algebraically. Since Lee and Lucas would have the same number of points at the solution to this system, you can set the expression for the number of points they each have, 80 − 12x and 20 + 3x, equal to one another. Do that now.
x
y
Lee
Lucas
0
1
2
3
4
5
6
7
8
9
10
0
8
16
24
32
40
48
56
64
72
80
Rounds
Points

20 + 3x =
80 − 12x
Nice!
You just found the point of intersection on the graph. Now, let's check that work algebraically. The expression for Lee's points has been set equal to the expression for Lucas's points. Solve the equation to find the value of x.
Lee's points = Lucas's points
80−12x
=
20+3x

x
=
Great job!
You just found that x = 4. That’s the same as the x-coordinate of the point of intersection. Let's see if the corresponding y-value is the same, too. You can use either equation. What’s the value of y when x = 4? You can solve on paper, and then enter your answer on Zearn.
y= 80 − 12x
y= 20 + 3x
When x= 4, y=
.
You got it!
You found that the point of intersection on the graph is (4, 32), and you solved algebraically to find that x = 4 and y = 32. What does the point (4, 32) mean in the context of this problem?
x
y
Lee
Lucas
0
1
2
3
4
5
6
7
8
9
10
0
8
16
24
32
40
48
56
64
72
80
Rounds
Points

Lee and Lucas both have 4 points after 32 rounds.

Lee has 32 points and Lucas has 4 points.

Lee and Lucas both have 32 points after 4 rounds.

Answer 1

The point \( (4, 32) \) means that after 4 rounds of the game, both Lee and Lucas have the same number of points, which is 32. So the correct interpretation is:

Lee and Lucas both have 32 points after 4 rounds.