The relationships between rounds played, x, and points, y, for Jiro and Lane are graphed on the coordinate plane below. What is the point of intersection?
x
y
Jiro
Lane
0
1
2
3
4
5
6
7
8
9
10
0
5
10
15
20
25
30
35
40
45
50
Rounds
Points
The point of intersection is (
,
).
Great job!
Now that you have found the point of intersection, (5, 40), let’s check that work algebraically. Since Jiro and Lane 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, 50 − 2x and 30 + 2x, equal to one another. Do that now.
x
y
Jiro
Lane
0
1
2
3
4
5
6
7
8
9
10
0
5
10
15
20
25
30
35
40
45
50
Rounds
Points
50 − 2x
=
30 + 2x
Nice!
You just found the point of intersection on the graph. Now, let's check that work algebraically. The expression for Jiro's points has been set equal to the expression for Lane's points. Solve the equation to find the value of x.
Jiro's points = Lane's points
50−2x
=
30+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= 50 − 2x
y= 30 + 2x
When x= 5, y=
.
Excellent!
You found that the point of intersection on the graph is (5, 40), and you solved algebraically to find that x = 5 and y = 40. What does the point (5, 40) mean in the context of this problem?
x
y
Jiro
Lane
0
1
2
3
4
5
6
7
8
9
10
0
5
10
15
20
25
30
35
40
45
50
Rounds
Points
Jiro and Lane both have 5 points after 40 rounds.
Jiro has 40 points and Lane has 5 points.
Jiro and Lane both have 40 points after 5 rounds.
1 answer
The point (5, 40) in the context of this problem means:
Jiro and Lane both have 40 points after 5 rounds.
This reflects the situation in the game where after playing 5 rounds, they end up with the same score of 40 points, regardless of how they started.
1 answer
1 answer
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1 answer