Question

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

Part A

What are the x-intercept and the y-intercept of the graph of her profit?

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

Consider the given linear equation,

`12x-4y=48`

PART A

Substitute y=0 to obtain the x-intercept,

`\begin{gathered} 12x-4(0)=48 \\ 12x=48 \\ x=4 \end{gathered}`

Thus, the x-intercept is 4 .

Substitute x=0 to obtain the y-intercept,

`\begin{gathered} 12\mleft(0\mright)-4y=48 \\ -4y=48 \\ y=-12 \end{gathered}`

Thus, the y-intercept is -12 .

Therefore, option C is the correct choice

PART B

The linear equation can also be written as,

`\begin{gathered} 4y=12x-48 \\ y=(12)/(4)x-(48)/(4) \\ y=3x-12 \end{gathered}`

The minimum limit to make a profit can be calculated as,

`\begin{gathered} y>0 \\ 3x-12>0 \\ 3x>12 \\ x>(12)/(3) \\ x>4 \end{gathered}`

Note that the order of photograph must be an integer. The next integer after 4 is 5.

So the minimum order size to make a profit should be 5.