Question

b. draw a line representing the relationship between x, the number of hours it takes the painting company to finish the house, and y, the total cost of painting the house. label the two points from the earlier question on your graph.

Explanation:

To solve this, we assume we have two points from the earlier question (e.g., let's say when \( x = 0 \), \( y = \text{fixed cost} \), and when \( x = h \), \( y = \text{total cost at } h \) hours). But since the earlier question's points aren't provided, we'll outline the general steps:

Step 1: Identify the two points

Let's assume from the earlier question, we have two points \((x_1, y_1)\) and \((x_2, y_2)\). For example, if the fixed cost is \( \$500 \) (when \( x = 0 \), \( y = 500 \)) and the cost per hour is \( \$50 \), then at \( x = 10 \) hours, \( y = 500 + 50(10) = 1000 \), so points are \((0, 500)\) and \((10, 1000)\).

Step 2: Plot the points

• Locate \( x_1 \) on the x - axis (hours) and \( y_1 \) on the y - axis (dollars), mark the point \((x_1, y_1)\).
• Locate \( x_2 \) on the x - axis and \( y_2 \) on the y - axis, mark the point \((x_2, y_2)\).

Step 3: Draw the line

Use a straight - edge to draw a line connecting the two plotted points. This line represents the linear relationship between the number of hours \( x \) and the total cost \( y \) (since the cost of painting a house is likely a linear function, \( y=\text{fixed cost}+\text{hourly rate}\times x\)).

Step 4: Label the points

Write the coordinates of the two points (from the earlier question) next to their respective plotted points on the graph.

Since the specific points from the "earlier question" are not provided, we can't draw the exact line, but the process involves plotting the two known points and drawing a line through them to represent the linear relationship between hours (x) and total cost (y).

If we assume a common scenario where the fixed cost is \( \$0 \) (unlikely, but for example) and the cost per hour is \( \$50 \), at \( x = 0 \), \( y = 0 \); at \( x = 20 \), \( y = 1000 \). We plot \((0,0)\) and \((20,1000)\) and draw a line through them.

The key is to use the two points from the previous problem, plot them on the given coordinate system (with x - axis from 0 to 60 and y - axis from 0 to 4000), and draw a straight line connecting them, then label the points with their coordinates.

(Note: Since the original problem doesn't provide the two points from the "earlier question", the above is a general method. If you can provide the two points from the earlier question, we can give a more precise drawing instruction.)

Answer:

To solve this, we assume we have two points from the earlier question (e.g., let's say when \( x = 0 \), \( y = \text{fixed cost} \), and when \( x = h \), \( y = \text{total cost at } h \) hours). But since the earlier question's points aren't provided, we'll outline the general steps:

Step 1: Identify the two points

Let's assume from the earlier question, we have two points \((x_1, y_1)\) and \((x_2, y_2)\). For example, if the fixed cost is \( \$500 \) (when \( x = 0 \), \( y = 500 \)) and the cost per hour is \( \$50 \), then at \( x = 10 \) hours, \( y = 500 + 50(10) = 1000 \), so points are \((0, 500)\) and \((10, 1000)\).

Step 2: Plot the points

• Locate \( x_1 \) on the x - axis (hours) and \( y_1 \) on the y - axis (dollars), mark the point \((x_1, y_1)\).
• Locate \( x_2 \) on the x - axis and \( y_2 \) on the y - axis, mark the point \((x_2, y_2)\).

Step 3: Draw the line

Use a straight - edge to draw a line connecting the two plotted points. This line represents the linear relationship between the number of hours \( x \) and the total cost \( y \) (since the cost of painting a house is likely a linear function, \( y=\text{fixed cost}+\text{hourly rate}\times x\)).

Step 4: Label the points

Write the coordinates of the two points (from the earlier question) next to their respective plotted points on the graph.

Since the specific points from the "earlier question" are not provided, we can't draw the exact line, but the process involves plotting the two known points and drawing a line through them to represent the linear relationship between hours (x) and total cost (y).

If we assume a common scenario where the fixed cost is \( \$0 \) (unlikely, but for example) and the cost per hour is \( \$50 \), at \( x = 0 \), \( y = 0 \); at \( x = 20 \), \( y = 1000 \). We plot \((0,0)\) and \((20,1000)\) and draw a line through them.

The key is to use the two points from the previous problem, plot them on the given coordinate system (with x - axis from 0 to 60 and y - axis from 0 to 4000), and draw a straight line connecting them, then label the points with their coordinates.

(Note: Since the original problem doesn't provide the two points from the "earlier question", the above is a general method. If you can provide the two points from the earlier question, we can give a more precise drawing instruction.)