A coach has 88 golf balls for the school's golf team. The coach will give each player on the team 11 golf balls. The graph shows the linear relationship between `y`, the number of golf balls remaining for the team, and `x`, the number of players on the team.
The equation of the line can be written as:
y = mx + b
Where m is the slope and b is the y-intercept.
From the problem, we know that the coach has 88 golf balls initially when there are no players on the team. This means that the y-intercept is 88.
So far, we have:
y = mx + 88
To find the slope, we can use the point-slope formula:
m = (y2 - y1)/(x2 - x1)
Let's choose two points on the line: (0, 88) and (x, y). The coordinates (0, 88) represent the scenario when there are no players and the team still has 88 golf balls. The coordinates (x, y) represent any other point on the line.
Replacing the coordinates in the formula, we have:
m = (y - 88)/(x - 0)
Simplifying:
m = (y - 88)/x
We also know from the problem that the coach will give each player 11 golf balls. Therefore, the number of golf balls remaining for the team, y, will be 88 minus 11 times the number of players, x.
Replacing y in the previous equation, we have:
m = ([88 - 11x] - 88)/x
Simplifying:
m = -11x/x
m = -11
Finally, replacing the value of m and b in the equation y = mx + b, we have:
y = -11x + 88
This is the equation of the line that represents the linear relationship between the number of golf balls remaining for the team, y, and the number of players on the team, x.