Since the function is linear, you can pick any two points to use for finding the parameters of the line. It can be convenient to use (9, 11.25) and (10, 12). Then we can start from the 2-point form of the equation for a line and simplify it to the expected slope-intercept form.
[tex]f(x)=\dfrac{(y_{2}-y_{1})}{(x_{2}-x_{1})}\cdot (x-x_{2}) +y_{2}\\\\f(x)=\dfrac{(12-11.25)}{(10-9)}\cdot (x-10)+12\\\\f(x)=0.75(x-10)+12\\\\f(x)=0.75x+4.50[/tex]
In this context, the slope is the variable cost, the cost of materials and labor that go into each card. The intercept is the fixed cost, the cost that must be paid to facilitate card-making, often for tools or workspace.
