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Slick Slack is a downloadable app that can be used to automatically generate excuses for being late to work based on the weather, traffic conditions, and the employer's line of business. One week after its release, 6,040 copies of Slick Slack were downloaded. After 5 weeks, 13,090 copies had been downloaded. Let x represent the number of weeks since Slick Slack was released, and y represent the number of copies that had been downloaded. Use the marginal change and the fact that 1 week after its release 5840 copies of Slick Slack were downloaded to determine the y intercept in the equation y = a + bx.
a) (x,y) =____.
b) write the equation in the form y = a + bx for the number of copies downloaded x weeks after its release.

Respuesta :

MrRoyal

Answer:

[tex](x_1,y_1) = (1,5840)[/tex]

[tex](x_2,y_2) = (2,13090)[/tex]

[tex]y = 1812.5x + 4027.5[/tex]

[tex]y_0 = 4027.5[/tex] --- y intercept

Step-by-step explanation:

Given:

x = weeks; y = copies

The right parameters are:

After 1 week, 5840 copies were downloaded

After 5 weeks, 13090 copies were downloaded

So, the (x,y) forms are:

[tex](x_1,y_1) = (1,5840)[/tex]

[tex](x_2,y_2) = (5,13090)[/tex]

Next, we calculate the slope (m) using:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \frac{13090 - 5840}{5 - 1}[/tex]

[tex]m = \frac{7250}{4}[/tex]

[tex]m = 1812.5[/tex]

The equation is then calculated using:

[tex]y = m(x - x_1) + y_1[/tex]

[tex]y = 1812.5(x - 1) + 5840[/tex]

[tex]y = 1812.5x - 1812.5 + 5840[/tex]

[tex]y = 1812.5x + 4027.5[/tex]

To calculate the y intercept, substitute 0 for x

[tex]y_0 = 1812.5*0 + 4027.5[/tex]

[tex]y_0 = 0 + 4027.5[/tex]

[tex]y_0 = 4027.5[/tex]

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