Question

Your team has carefully researched and selected two possible painting companies. Pro Painters charge $200 per hour plus $6000 in material fees. Illusion Ltd charges $150 per hour plus $8000 in material fees.Create a graph of the cost for both companies using the grid below. Circle the point of intersection. Be sure your lines are properly identified.

Answer 1

Given:

• Pro Painters:

Charge per hour = $200

Material fees = $6000

• Illusion Ltd:

Charge per hour = $150

Material fees = $8000

Let's create a graph of the cost for both companies.

Represent each situation using the slope-intercept form:

y = mx + b

In this case, y represents the total charge, m is the charge per hour, x represents the number of hours, and b represents the material fees.

We have the following:

• Equation for Pro Painters:

y = 200x + 6000

• Equation for Illsion Ltd:

y = 150x + 8000

To graph let's create two points on each equation.

We have:

• Pro painters:

y = 200x + 6000

When x = 1: y = 200(10) + 6000 = 8000

When x = 3: y = 200(30) + 6000 = 12000

We have the points:

(x, y) ==> (10, 8000), (30, 12000)

Plot the points and connect them using a straight line.

• Illusion Ltd:

y = 150x + 8000

When x = 2: y = 150(20) + 8000 = 11000

When x = 4: y = 150(40) + 8000 = 14000

We have the points:

(x, y) ==> (20, 11000), (40, 14000)

Plot the points and connect them using a straight line.

We have the graph below:

The green line represents the cost for Pro Painters

The blue line represents the cost for Illusion Ltd.

From the graph, the point of intersection is (40, 14000).

This means at 40 hours, the cost for both companies will be the same ($14,000)

ANSWER:

• Equation for Pro painters: , y = 200x + 6000

,

• Equation for Illusion Ltd: , y = 150x + 8000

,

• Point of intersection: (40, 14000)