How do I model "A market sells chicken for $2.99 a pound" with a linear function and graph?
Let x = weight of chicken in pounds
Let y = total cost of x pounds of chicken
Therefore,
y = 2.99x
To see the graph of this, go to wolframalpha . com and type in the equation.
Hope this helps :3wol
To model the given scenario with a linear function and graph, we need to understand the relationship between the weight of chicken and its cost. In this case, the cost of chicken depends on the weight, so we can use a linear equation of the form y = mx + b, where y represents the cost, x represents the weight, m represents the slope, and b represents the y-intercept.
Given that the market sells chicken for $2.99 a pound, we know that when the weight (x) is 0, the cost (y) is also $0. Therefore, the y-intercept, b, is 0.
The price of chicken remains constant at $2.99 per pound, which means the slope, m, is also $2.99.
Now, we can write the linear equation as:
y = 2.99x
To graph this equation, we can plot several points on the coordinate plane and then connect them with a straight line. For example, we can choose weights of 1 pound, 2 pounds, 3 pounds, and so on, and find the corresponding costs:
When x = 1, y = 2.99 * 1 = $2.99
When x = 2, y = 2.99 * 2 = $5.98
When x = 3, y = 2.99 * 3 = $8.97
Plot these points: (1, $2.99), (2, $5.98), (3, $8.97), and so on.
Then, connect the points with a straight line. Remember that since the y-intercept is 0, the line will pass through the origin (0,0).
Here's a visual representation of the graph:
(please imagine a graph)
The x-axis represents the weight of the chicken in pounds, and the y-axis represents the cost of chicken in dollars. The line passes through the origin and increases steadily with a slope of $2.99.
By using the linear function y = 2.99x and graphing it, we have modeled the scenario where a market sells chicken for $2.99 a pound.