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=
.
1 answer
To find the value of \(y\) when \(x = 4\), we can use either equation for Lee's points or Lucas's points. Let's use both for verification.
For Lee's points: \[ y = 80 - 12x \] Substituting \(x = 4\): \[ y = 80 - 12(4) \] \[ y = 80 - 48 \] \[ y = 32 \]
For Lucas's points: \[ y = 20 + 3x \] Substituting \(x = 4\): \[ y = 20 + 3(4) \] \[ y = 20 + 12 \] \[ y = 32 \]
In both cases, when \(x = 4\), the value of \(y\) is 32.
So the final answer is \(y = 32\).
