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
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30
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50
60
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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
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9
10
0
10
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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=
.
Great job!
You found that the point of intersection on the graph is (5, 60), and you solved algebraically to find that x = 5 and y = 60. What does the point (5, 60) mean in the context of this problem?
x
y
Jack
Bill
0
1
2
3
4
5
6
7
8
9
10
0
10
20
30
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50
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Rounds
Points
Jack and Bill both have 60 points after 5 rounds.
Jack and Bill both have 5 points after 60 rounds.
Jack has 60 points and Bill has 5 points.
1 answer
The point of intersection (5, 60) means that after 5 rounds of the game, both Jack and Bill have the same number of points, which is 60 points each. Thus, the correct interpretation in the context of this problem is:
Jack and Bill both have 60 points after 5 rounds.
1 answer
1 answer
1 answer
1 answer