Step-by-step explanation:
Given:
- total score is 63
- field goals score 3
- touchdowns score 7
Find:
- a linear equation representing the relationships given
- a graph of that equation
- combinations of field goals and touchdowns that give the score
Solution:
1. see above for what is given
2. Touchdowns and field goals can be represented by variables. In the attachment, field goals are represented by x, and touchdowns are represented by y.
The score value of a field goal is 3, so the total score from x field goals can be written as the term 3x.
Likewise, the total score from y touchdowns can be written as the term 7y.
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The equation of interest is then ...
3x + 7y = 63
The graph of it, and its integer solutions, is attached.
Possible combinations of (field goals, touchdowns) are ...
(0, 9), (7, 6), (14, 3), (21, 0)