Johnny pays for a music streaming service, where he is billed $5 each month and $1 per song download. Which of the following graphs best models how much Johnny is going to pay for one month?(1 point)
Responses
The graph of a linear equation best models how much Johnny is going to pay for one month.
To determine how much Johnny is going to pay for one month, we need to consider the fixed monthly charge of $5 and the variable charge of $1 per song download.
One way to graphically represent this situation is with a piecewise function. Let's assume that x represents the number of song downloads in a month.
- For 0 ≤ x ≤ 1, the total cost can be represented as: f(x) = 5 (monthly charge) + 1 (variable charge per song download) * x
This means that the total cost is the fixed monthly charge of $5 plus the variable charge of $1 per song download.
- However, since the question specifically asks for a graph, we can simplify this equation further by assuming Johnny can only download whole numbers of songs (0, 1, 2, 3,...).
Given these conditions, the best graph representing how much Johnny will pay for one month is a step function graph. This graph will have a horizontal line segment at y = 5 (representing the fixed monthly charge), and another horizontal line segment starting at (1, 6) with a slope of 1 (representing the variable charge per song download).
The correct response option would be the graph that represents a step function with a horizontal line segment at y = 5 and another horizontal line segment starting at (1, 6) with a slope of 1.
Since Johnny is billed $5 each month and $1 per song download, we can use a linear equation to represent the total cost.
Let's represent the number of song downloads as x.
The equation will be y = 5 + x.
To graph this equation, we can plot points on a graph.
Let's consider a few scenarios:
- If Johnny doesn't download any songs (x = 0), the total cost would be $5 (y = 5).
- If Johnny downloads 1 song (x = 1), the total cost would be $6 (y = 6).
- If Johnny downloads 2 songs (x = 2), the total cost would be $7 (y = 7).
We can continue to calculate more points and plot them on a graph.
Based on the information above, the graph that best models how much Johnny is going to pay for one month is a line with a slope of 1 and a y-intercept of 5.