Question

If a ship's path is mapped on a coordinate grid, it follows a straight-line path of slope 3 and passes through point (2, 5).

Part A: Write the equation of the ship’s path in slope-intercept form. (2 points)

Part B: A second ship follows a straight line, with the equation x + 3y − 6 = 0. Are these two ships sailing perpendicular to each other? Justify your answer. (2 points)

Answer 1

Part A: The equation of the ship's path is
`y=3x-1`

Part B: The two ships sails perpendicular to each other.

Step-by-step explanation:

Part A: It is given that
`m=3` and point (2, 5)

Substituting these in the slope intercept form, we have,

`y-y_(1)=m\left(x-x_(1)\right)`

`\begin{aligned}y-5 &=3(x-2) \\y-5 &=3 x-6 \\y &=3 x-1\end{aligned}`

Thus, the equation of the ship's path in slope intercept form is
`y=3x-1`

Part B: The equation of the second ship is
`x+3 y-6=0`

Let us bring the equation in the form of slope intercept form.

`\begin{aligned}3 y &=-x+6 \\y &=-(1)/(3) x+2\end{aligned}`

Thus, from the above equation the slope is
`m=-(1)/(3)`

To determine the two ships sailing perpendicular to each other, we have

`m_(1) * m_(2)=-1`

where
`m_(1)=3` and
`m_(2)=-(1)/(3)`

`\begin{aligned}3 *-(1)/(3) &=-1 \\-1 &=-1\end{aligned}`

Since, both sides of the equation are equal, these two ships sails perpendicular to each other.