Question

A linear function has the table of values shown. The information in the table shows the number of tickets sold on opening night of a movie as a function of the number of hours since the tickets have been on sale. Number of Hours (x) 2 6 18
Number of Tickets Sold (y) 64 192 576

1.Write the equation that gives the number of tickets sold, y, as a linear function of the number of hours, x, since the tickets have been on sale.

Answer 1

The equation that represents the linear function is y =32x

What is a linear function?

The question is an illustration of a linear function; a linear function is a function that has a constant rate/slope

A linear function is represented as:

$y=mx+c$

Where

• m represents slope
• c represents the y-intercept

The slope is calculated as:

$m = \frac{y_2 -y_1}{x_2 -x_1}$

So, we have:

$m = \frac{576 - 64}{18-2}$

$m = \frac{512}{16}$

$m = 32$

The linear equation is then calculated as:

$y =m(x -x_1) + y_1$

So, we have:

$y =32(x -2) + 64$

$y =32x -64 + 64$

$y =32x$

Hence, the equation that represents the linear function is y =32x

Read more about linear functions at:

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