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). Par

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)

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Raelynn 1 week 2022-01-08T16:58:34+00:00 1 Answer 0 views 0

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    2022-01-08T16:59:52+00:00

    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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