Please help me with this problem! I've been on it for hours.

Question

A football team scores 63 points. All of the points come from field goals worth 3 points and touchdowns worth 7 points. List every combination possible of field goals and touchdowns. Graph a linear equation that represents this situation. *Explain the advantages and disadvantages of graphing this situation...*

My problem with this is how I am supposed to get the possible combination. Do you need to write it in a linear equation first? And with the linear equation, do you need to plug in the combinations that we are going to find?

Answer 1

63 = 3x + 7y

If x = 0, then y = 9

If x = 1, then y = 60/7, which is not a whole number

If x = 2, then y = 57/7 not a whole number

If x = 3, then y = 54/7 not a whole number

If x = 4, then y = 51/7 not a whole number

If x = 5, then y = 48/7 not a whole number

If x = 6, then y = 45/7 not a whole number

If x = 7, then y = 42/7 = 6

If x = 8, then y = 39/7 not a whole number

If x = 9, then y = 36/7 not a whole number

If x = 10, then y = 33/7 not a whole number

If x = 11, then y = 30/7 not a whole number

If x = 12, then y = 27/7 not a whole number

If x = 13, then y = 24/7 not a whole number

If x = 14, then y = 21/7 = 3

If x = 15, then y = 18/7 not a whole number

If x = 16, then y = 15/7 not a whole number

If x = 17, then y = 12/7 not a whole number

If x = 18, then y = 9/7 not a whole number

If x = 19, then y = 6/7 not a whole number

If x = 20, then y = 3/7 not a whole number

If x = 21, then y = 0

y = mx + b

m = (0 - 3)/(21 - 14) = -3/7

y = -3/7(x) + b

0 = (-3/7)21 + b

0 = -9 + b

b = 9

y = (-3/7)x + 9

This is the linear equation. Graph using points in bold above.