Linear Applications:Standard Form

Read the problem carefully.

Define the variables.

Write the equation in standard form.

Solve for the x-intercept by substituting in zero for y.

Solve for the y-intercept by substituting in zero for x.

Plot the intercepts.

Graph the line.

Answer the problem.

The student government is sponsoring apancake dinner to raise money for a fieldtrip. The officers estimate that 200 adultsand 300 children will attend. Write an equation, graph the line, and determinereasonable ticket prices to set in order to raise $4200.

The student government is sponsoring a pancake dinner to raise money for a field trip. The officers estimate that 200 adults and300 children will attend. Write an equation, graph the line, anddetermine reasonable ticket prices to set in order to raise $4200.

Step 1: Read the problem carefully.

Step 2: Define the variables.

Let x = cost of an adult ticketLet y = cost of a student ticket

Step 3: Write the equation in standard form.

200x + 300y = 4200

Step 4: Solve for the x-intercept by substituting in zero for y.

200x + 300(0) = 4200200x = 4200x = 21

Step 5: Solve for the y-intercept by substituting in zero for x.

200(0) + 300y = 4200300y = 4200x = 14

So the x intercept is (21,0) and the y intercept is (0, 14).

Step 6: Plot the intercepts.Step 7: Graph the line.

Step 8: Answer the question. What are reasonable ticket prices?

You are running a concession stand at the basketball game. You sell hot dogs for $1 and sodas for $0.50. At the end of the night, you made $200. Write an equation, graph the line, and determine the possible number of hot dogs and sodas that were sold.

You are running a concession stand at the basketball game. You sell hot dogs for $1 and sodas for $0.50. At the end of the night, you made $200. Write an equation, graph the line, and determine the possible number of hot dogs and sodas that were sold.

Step 1: Read the problem carefully.

Step 2: Define the variables.

Let x = # of hot dogs soldLet y = # of sodas sold

Step 3: Write the equation in standard form.

1x + 0.50y = 200

Step 4: Solve for the x-intercept by substituting in zero for y.

1x + 0.50(0) = 2001x = 200x = 200

Step 5: Solve for the y-intercept by substituting in zero for x.

1(0) + 0.50y = 2000.50y = 200y = 400

So the x intercept is (200,0) and the y intercept is (0, 400).

Step 6: Plot the intercepts.Step 7: Graph the line.

Step 8: Answer the question. What combination of hot dogs/sodas could have been sold?