Jack and Bill are playing a computer game. Jack has 90 points and loses 6 points each round. Bill has 50 points and earns 2 points each round.

Question

The relationships between rounds played, x, and points, y, for Jack and Bill are graphed on the coordinate plane below. What is the point of intersection?
x
y
Jack
Bill
0
1
2
3
4
5
6
7
8
9
10
0
10
20
30
40
50
60
70
80
90
100
Rounds
Points
The point of intersection is (
,
).
Excellent!
Now that you have found the point of intersection, (5, 60), let’s check that work algebraically. Since Jack and Bill 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, 90 − 6x and 50 + 2x, equal to one another. Do that now.
x
y
Jack
Bill
0
1
2
3
4
5
6
7
8
9
10
0
10
20
30
40
50
60
70
80
90
100
Rounds
Points

90 − 6x
=
50 + 2x
Good work!
You just found the point of intersection on the graph. Now, let's check that work algebraically. The expression for Jack's points has been set equal to the expression for Bill's points. Solve the equation to find the value of x.
Jack's points = Bill's points
90−6x
=
50+2x

x
=
Excellent!
You just found that x = 5. 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 = 5? You can solve on paper, and then enter your answer on Zearn.
y= 90 − 6x
y= 50 + 2x
When x= 5, y=
.

Answer 1

To find the value of \( y \) when \( x = 5 \), we can use either equation. Let's use both equations to verify.

1. Using Jack's points equation: \[ y = 90 - 6x \] Substituting \( x = 5 \): \[ y = 90 - 6(5) = 90 - 30 = 60 \]

2. Using Bill's points equation: \[ y = 50 + 2x \] Substituting \( x = 5 \): \[ y = 50 + 2(5) = 50 + 10 = 60 \]

In both cases, when \( x = 5 \), \( y = 60 \).

So, when \( x = 5 \), \( y = 60 \).

Thus, the answer is \( y = 60 \).