Question

Harriet sells prints of her photographs and is deciding what her minimum order should be during a sale. The equation that relates her profit y, from an order of size x is 12x – 4y = 48.

Part A

What are the x and the y-intercepts of the graph of her equation?
A. x-intercept: 3; y-intercept: –12
B. x-intercept: 4; y-intercept: 12
C. x-intercept: 4; y-intercept: –12
D. x-intercept: 3; y-intercept: 12
Part B

What should her minimum order size be, to make a profit?

Answer 1

To solve Part A, we need to find the x-intercept and the y-intercept of the equation \( 12x - 4y = 48 \).

**Finding the x-intercept:**
The x-intercept occurs when \( y = 0 \).

Substituting \( y = 0 \) into the equation:
\[
12x - 4(0) = 48 \\
12x = 48 \\
x = \frac{48}{12} = 4
\]
So, the x-intercept is 4.

**Finding the y-intercept:**
The y-intercept occurs when \( x = 0 \).

Substituting \( x = 0 \) into the equation:
\[
12(0) - 4y = 48 \\
-4y = 48 \\
y = \frac{48}{-4} = -12
\]
So, the y-intercept is -12.

Therefore, the x-intercept is 4 and the y-intercept is -12. The correct answer is **C. x-intercept: 4; y-intercept: –12**.

---

For Part B, we need to determine the minimum order size, \( x \), required to make a profit. A profit typically means that \( y \) is greater than 0.

Rearranging the original equation \( 12x - 4y = 48 \) to find \( y \):
\[
-4y = 48 - 12x \\
4y = 12x - 48 \\
y = 3x - 12
\]

To find when profit begins (where \( y > 0 \)):
\[
3x - 12 > 0 \\
3x > 12 \\
x > \frac{12}{3} \\
x > 4
\]

This means that the minimum order size \( x \) should be greater than 4 to make a profit. Thus, Harriet's minimum order size to make a profit should be at least **5**.