D. Solving Problems using General Form

The general form of a linear equation is also useful for modelling some scenarios. A closely related form, Ax + By = D, can be used when two values add to a known total. This form can be interpreted using the same strategies that applied to the general form.



Example 1

Carlos is renovating his house and is transporting materials home from the hardware store. His truck has a load capacity of 1 000 lbs. He plans to move sheets of drywall weighing 40 lbs each, and sheets of plywood weighing 50 lbs each.

  1. Write the equation of a linear relation that represents the number of sheets of drywall and plywood that Carlos can carry in each load.

  2. Sketch the graph of this relation.

  3. State the domain and range of the graph of the relation.

  4. If Carlos only needs 7 sheets of plywood, how many sheets of drywall can he carry?

  1. Write the equation of a linear relation that represents the number of sheets of drywall and plywood that Carlos can carry in each load.

    Let d represent the number of sheets of drywall and let p represent the number of sheets of plywood. This means the total weight of the drywall can be represented as 40 d and the total weight of the plywood can be represented as 50 p.



  2. Sketch the graph of this relation.

    The intercepts can be used to sketch the graph.



    The     p -intercept is 20.



    The     d -intercept is 25.

  3. State the domain and range of the graph of the relation.




  4. If Carlos only needs 7 sheets of plywood, how many sheets of drywall can he carry?



    Carlos will be able to carry 16 sheets of drywall in addition to the 7 sheets of plywood.