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Carlos was driving at a constant speed. After three hours he was three hundred miles from E-Town on the highway at the 6 hours he was full and 80 miles from town which fraction which function represents Carlos distance y from the town after X hours

Sagot :

MrRoyalidn

Answer:

[tex]y = -\frac{220}{3}x + 520[/tex]

Step-by-step explanation:

Given

[tex]x = time[/tex]

[tex]y = distance[/tex]

For the first 3 hours, we have:

[tex](x_1,y_1) = (3,300)[/tex]

At 6 hours, we have:

[tex](x_2,y_2) = (6,80)[/tex]

Required

Express y as a function of x

First, calculate the slope:

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

This gives:

[tex]m = \frac{80 - 300}{6 - 3}[/tex]

[tex]m = \frac{-220}{3}[/tex]

[tex]m = -\frac{220}{3}[/tex]

The equation is then calculated using:

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

Where:

[tex]m = -\frac{220}{3}[/tex]

[tex](x_1,y_1) = (3,300)[/tex]

[tex]y = -\frac{220}{3}(x - 3) + 300[/tex]

Open bracket

[tex]y = -\frac{220}{3}x + \frac{220}{3}*3 + 300[/tex]

[tex]y = -\frac{220}{3}x + 220 + 300[/tex]

[tex]y = -\frac{220}{3}x + 520[/tex]

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