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The graph represents revenue in dollars as a function of greeting cards sold.

A coordinate plane showing Greeting Card Revenue, Number of Cards Sold on the x-axis and Revenue in dollars on the y-axis. A line starts at (0. 0) and passes through (2, 8), (4, 16), and ends at (5, 20).

Which equation represents the function shown on the graph?

y = x
y = x
y = 2x
y = 4x

1 answer

To determine which equation represents the revenue as a function of greeting cards sold, we can analyze the points provided in the graph.

The points given are:

  • (0, 0)
  • (2, 8)
  • (4, 16)
  • (5, 20)

These points indicate a linear relationship. To find the equation of the line, we can derive the relationship between the number of cards sold (x) and the revenue generated (y).

From the points:

  • When 2 cards are sold, revenue is 8 dollars.
  • When 4 cards are sold, revenue is 16 dollars.
  • When 5 cards are sold, revenue is 20 dollars.

To find the slope (m) of the line, we can use the formula for slope, which is:

\[ m = \frac{(y_2 - y_1)}{(x_2 - x_1)} \]

Using the points (2, 8) and (4, 16): \[ m = \frac{(16 - 8)}{(4 - 2)} = \frac{8}{2} = 4 \]

So the slope (m) is 4.

The equation of a line in slope-intercept form is given as: \[ y = mx + b \] where b is the y-intercept.

Since the line passes through the origin (0, 0), the y-intercept (b) is 0. Therefore, the equation simplifies to:

\[ y = 4x \]

Thus, the equation that represents the function shown on the graph is:

\[ y = 4x \]