Answer: The answer is (A) [tex] y=-\dfrac{1}{3}x-2.[/tex]
Step-by-step explanation: Given that Michael cuts a piece of wood for a project . The first cut is shown in the given figure and represented by the equation [tex]y=-\dfrac{1}{3}x+6.[/tex] The second cut should be parallel to the first one and will pass through the point (0, -2). We are to find the equation of the second cut.
The equation of the first cut is
[tex]y=-\dfrac{1}{3}x+6.[/tex]
So, slope will be
[tex]m_1=-\dfrac{1}{3}.[/tex]
Since the second cut is parallel to the first one, so the slope of the second cut will be equal to the slope of the first one. Also, the second cut passes through the point (0, -2), so its equation will be
[tex] y-(-2)=-\dfrac{1}{3}(x-0)\\\\\Rightarrow y+2=-\dfrac{1}{3}x\\\\\Rightarrow y=-\dfrac{1}{3}x-2.[/tex]
Thus, (A) is the correct option.
