**6. To determine which combinations of sketchbooks and paint sets Alex can purchase using her $96.00 gift card, we need to formulate the equation based on the costs of each item.
Let \( x \) be the number of sketchbooks and \( y \) be the number of paint sets. The total cost can be expressed as: \[ 12x + 15y = 96 \]
Now we can evaluate each of the options:
A) 2 sketchbooks and 5 paint sets: \[ 12(2) + 15(5) = 24 + 75 = 99 \] (not valid)
B) 1 sketchbook and 4 paint sets: \[ 12(1) + 15(4) = 12 + 60 = 72 \] (valid but under budget)
C) 4 sketchbooks and 3 paint sets: \[ 12(4) + 15(3) = 48 + 45 = 93 \] (valid but under budget)
D) 3 sketchbooks and 4 paint sets: \[ 12(3) + 15(4) = 36 + 60 = 96 \] (valid and uses entire budget)
Only D) 3 sketchbooks and 4 paint sets allows Alex to spend her entire gift card of $96.00.
7. To determine whether the point (0, −3) is a solution to the inequality \( y > \frac{4}{5}x - 3 \), we can substitute \( x = 0 \) and \( y = -3 \) into the inequality:
Substituting into the inequality gives: \[ -3 > \frac{4}{5}(0) - 3 \] \[ -3 > -3 \]
This statement is false because -3 is not greater than -3.
Thus, the correct option is: A) No, because (0, −3) falls on the dashed boundary line (the inequality does not include equality because of the 'greater than' sign).