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Jobisdone [24]
3 years ago
6

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).

Mathematics
1 answer:
Ugo [173]3 years ago
3 0

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

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

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 &=-\frac{1}{3} x+2\end{aligned}

Thus, from the above equation the slope is m=-\frac{1}{3}

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

m_{1} \times m_{2}=-1

where m_{1}=3 and m_{2}=-\frac{1}{3}

\begin{aligned}3 \times-\frac{1}{3} &=-1 \\-1 &=-1\end{aligned}

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

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