Jamie ordered 200 business cards and paid $23 short of 500 business cards a few months later and paid $35 write and solve a linear equation to find the cost to order 700 business card

  $43

Step-by-step explanation:

The 2-point form of the equation for a line is useful for this. It tells you ...

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

for a line through (x1, y1) and (x2, y2).

The points we are given are (200, 23) and (500, 35). We want to find the value of y for x=700. Putting all those numbers into the above equation gives ...

  y = (35 -23)/(500 -200)(700 -200) + 23 . . . . . the linear equation

  y = 12/300·500 +23 = 43 . . . . . . the solution

The cost to order 700 cards is $43.

It isn't clear what is intended here. In general, a linear equation describing the problem will have two unknowns. You are given two data points, so can write and solve a system of two equations to find those unknowns. Then to find the order cost, you must use the linear equation you found with the new value of the independent variable.

By using the two-point form of the equation and filling in the new value of the independent variable, we have collapsed those three steps into a single expression evaluation. We doubt that is what is intended, but we don't know what the intention is.