Question

this graph shows how the amount of concrete that bernie’s construction has left is related to the number of foundations that the company pours. how many foundations does bernies construction need to pour in order to have just 200 tons of concrete left?

Explanation:

Step1: Analyze the graph

The graph is a linear graph with the y - axis representing the amount of concrete remaining (in tons) and the x - axis representing the number of foundations. The line starts at (0, 800) and ends at (600, 0). We need to find the x - value when y = 200.

Step2: Find the slope of the line

The slope \(m\) of a line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Here, \((x_1,y_1)=(0,800)\) and \((x_2,y_2)=(600,0)\). So \(m=\frac{0 - 800}{600 - 0}=\frac{- 800}{600}=-\frac{4}{3}\).

Step3: Write the equation of the line

Using the slope - intercept form \(y=mx + b\), where \(b\) is the y - intercept. We know \(m =-\frac{4}{3}\) and \(b = 800\) (since the line crosses the y - axis at (0, 800)). So the equation is \(y=-\frac{4}{3}x + 800\).

Step4: Solve for x when y = 200

Substitute \(y = 200\) into the equation:

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Alternatively, we can use the concept of similar triangles or proportionality. The total change in concrete is \(800-0 = 800\) tons for 600 foundations. The change in concrete from 800 tons to 200 tons is \(800 - 200=600\) tons. Let the number of foundations be \(x\). We can set up a proportion: \(\frac{600}{800}=\frac{x}{600}\) (since the rate of change of concrete with respect to foundations is constant). Cross - multiplying gives \(800x=600\times600\), \(x=\frac{600\times600}{800}=\frac{360000}{800} = 450\).

Answer:

450