Respuesta :
Part A: The equation of the ship's path is [tex]y=3x-1[/tex]
Part B: The two ships sails perpendicular to each other.
Explanation:
Part A: It is given that [tex]m=3[/tex] and point (2, 5)
Substituting these in the slope intercept form, we have,
[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]
[tex]\begin{aligned}y-5 &=3(x-2) \\y-5 &=3 x-6 \\y &=3 x-1\end{aligned}[/tex]
Thus, the equation of the ship's path in slope intercept form is [tex]y=3x-1[/tex]
Part B: The equation of the second ship is [tex]x+3 y-6=0[/tex]
Let us bring the equation in the form of slope intercept form.
[tex]\begin{aligned}3 y &=-x+6 \\y &=-\frac{1}{3} x+2\end{aligned}[/tex]
Thus, from the above equation the slope is [tex]m=-\frac{1}{3}[/tex]
To determine the two ships sailing perpendicular to each other, we have
[tex]m_{1} \times m_{2}=-1[/tex]
where [tex]m_{1}=3[/tex] and [tex]m_{2}=-\frac{1}{3}[/tex]
[tex]\begin{aligned}3 \times-\frac{1}{3} &=-1 \\-1 &=-1\end{aligned}[/tex]
Since, both sides of the equation are equal, these two ships sails perpendicular to each other.
