A small appliance manufacturer finds that if he produces x toaster ovens in a month his production cost is given by the equation y=6x+3000 where y is measured in dollars
Sketch a graph of this linear equation
What does the slope of the graph represent
What does the y intercept of the graph represent
To sketch the graph of the equation y = 6x + 3000, we can start by plotting two points on the coordinate plane.
First, let's choose an arbitrary value for x and calculate the corresponding value of y using the equation. Let's assume x = 0.
When x = 0, y = 6(0) + 3000 = 3000. So the point (0, 3000) is one point on the graph.
Next, let's choose another value for x and calculate the corresponding value of y. Let's assume x = 500.
When x = 500, y = 6(500) + 3000 = 6000 + 3000 = 9000. So the point (500, 9000) is another point on the graph.
Now we can plot these two points and draw a straight line passing through them. The graph should extend in both directions.
The slope of the graph represents the rate of change of the production cost per unit of toaster ovens. In this case, the slope is 6. This means that for every unit increase in the number of toaster ovens produced, the production cost increases by $6.
The y-intercept of the graph represents the fixed cost, which is the cost incurred by the manufacturer even if no toaster ovens are produced. In this case, the y-intercept is 3000, so the fixed cost is $3000.
To sketch the graph of the linear equation y = 6x + 3000, we need to plot some points on a coordinate plane.
Let's choose a few values for x and calculate the corresponding y-values using the equation:
When x = 0, y = 6(0) + 3000 = 3000
When x = 500, y = 6(500) + 3000 = 6000 + 3000 = 9000
When x = 1000, y = 6(1000) + 3000 = 6000 + 3000 = 12000
Plotting the points (0, 3000), (500, 9000), and (1000, 12000), we can connect them with a straight line.
Now, let's interpret the slope and y-intercept:
The slope of the graph, 6, represents the cost per unit, which is the increase in production cost for each additional toaster oven produced. It indicates how much the cost (y) increases for each unit increase in the number of toaster ovens (x).
The y-intercept of the graph, 3000, represents the fixed cost component. It is the cost incurred even when no toaster ovens are produced. In this case, it represents the base cost of production that includes factors such as overhead costs and other fixed expenses.