A particle is moving along the line `5y=-6x+30` at a rate of 2 units per second. If the particle starts at the y-intercept and moves to the right along this line, how many seconds will it take for the particle to reach the x - axis ?

Options

A. `2.50`
B. `3.25`
C. `3.76`
D. `3.91`

Answer

D

Explanation

First find the distance from the starting point to the endpoint. The starting point is the y - intercept, which is easy to get if you put the give equation in slope - intercept form :
`5y=6x+30`
`y = -(6)/(5)x + 6`
The y - intercept is the point (0, 6). The x - intercept is the point at which y = 0 :
`5(0)=-6x+30`
6x = 30
x = 5
So, the x - intercept is the point (5, 0). The distance between those points is
Distance `= sqrt((y_(2)-y_(1))^(2)+(x_(2)-x_(1))^(2))`
`= sqrt((0-6)^(2)+(5-0)^(2))`
`= sqrt(36+25)`
`= sqrt(61)~~7.81`
At a rate of 2 units per second, it will take `(7.81)/(2)` seconds to travel 7.81 units. That's about 3.91.