Question

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

Answer 1

Answer:

$y = -\frac{220}{3}x + 520$

Step-by-step explanation:

Given

$x = time$

$y = distance$

For the first 3 hours, we have:

$(x_1,y_1) = (3,300)$

At 6 hours, we have:

$(x_2,y_2) = (6,80)$

Required

Express y as a function of x

First, calculate the slope:

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

This gives:

$m = \frac{80 - 300}{6 - 3}$

$m = \frac{-220}{3}$

$m = -\frac{220}{3}$

The equation is then calculated using:

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

Where:

$m = -\frac{220}{3}$

$(x_1,y_1) = (3,300)$

$y = -\frac{220}{3}(x - 3) + 300$

Open bracket

$y = -\frac{220}{3}x + \frac{220}{3}*3 + 300$

$y = -\frac{220}{3}x + 220 + 300$

$y = -\frac{220}{3}x + 520$