Answer:
B ![3x-2y=10](https://tex.z-dn.net/?f=3x-2y%3D10)
Step-by-step explanation:
This is correct because when solved it has the same slope as line <em>k.</em>
The slope of <em>k</em> is 3/2.
![3x-2y=10](https://tex.z-dn.net/?f=3x-2y%3D10)
first subtract 3x from both sides
![-2y=-3x+10](https://tex.z-dn.net/?f=-2y%3D-3x%2B10)
next divide both sides by -2
![y=3/2x-5](https://tex.z-dn.net/?f=y%3D3%2F2x-5)
this shows that the slope 3/2 is the same as line <em>k</em>
Its 1/7 because parallel lines have the same slope
First we will convert those radian angles to degrees, since my mind works better with degrees. Let's work one at a time. First,
![\frac{7 \pi }{4} * \frac{180}{ \pi }=315](https://tex.z-dn.net/?f=%20%5Cfrac%7B7%20%5Cpi%20%7D%7B4%7D%20%2A%20%5Cfrac%7B180%7D%7B%20%5Cpi%20%7D%3D315%20)
. If we start at the positive x-axis and measure out 315 we end up in the 4th quadrant with a reference angle of 45 with the positive x-axis. The side across from the reference angle is -1, the side adjacent to the angle is 1, and the hypotenuse is sqrt2. The cotangent of this angle, then is 1/-1 which is -1. As for the second one, converting radians to degrees gives us that
![\frac{13 \pi }{6} * \frac{180}{ \pi } =390](https://tex.z-dn.net/?f=%20%5Cfrac%7B13%20%5Cpi%20%7D%7B6%7D%20%2A%20%5Cfrac%7B180%7D%7B%20%5Cpi%20%7D%20%3D390)
. Sweeping out that angle has us going around the origin more than once and ending up in the first quadrant with a reference angle of 30° with the positive x-axis. The side across from the angle is 1, the side adjacent to the angle is √3, and the hypotenuse is 2. Therefore, the secant of that angle is 2/√3.