Question

Narek and his family are driving home from vacation and

plan on taking their time. They drive the same amount of
miles every day. After 4 days of driving, they are 400
miles from home. After 8 days of driving, they are 250
miles from home. Let x represent the number of days
Narek and his family are driving home from vacation and
y represent how far away from home (in miles) they are.

Answer 1

The answer is below

Explanation:

Let x represent the number of days Narek and his family are driving home from vacation and y represent how far away from home (in miles) they are.

Narek and his family vacation can be represented by coordinate points (x, y) as (4, 400) and (8, 250). We can get an equation using this formula:

`y-y_1=(y_2-y_1)/(x_2-x_1) (x-x_1)\\\\Hence:\\\\y-400=(250-400)/(8-4)(x-4)\\\\y-400=-37.5(x-4)\\\\y-400=-37.5x +150\\\\y=-37.5x +550`

The x intercept is the value of x when y = 0:

0 = -37.5(x) + 550

37.5x = 550

x=14.7

The y intercept is the value of y when x = 0:

y = -37.5(0) + 550

y = 550

Therefore the x intercept is 14.7. Which means that when Narek and his family drive for 14.7 days, they are 0 miles from home.

Therefore the y intercept is zero. Which means that when Narek and his family drive for 0 days, they are 550 miles from home.

Comparing the above equation with the equation of a straight line y = mx + b, where m is the slope and b the y intercept, we can get that the slope (m) is -37.5.

The slope is -37.5. This means that for every one day, they have 37.5 miles less to drive to get home.