Use the Slope and \( y \)-Intercept sliders to graph the line \( y=6 x-2 \). Check the Show 2nd Line box and click and move the red point to graph a parallel line \( L \) through the point \( (2,1) \). Use the interactive figure to find your answer. Use the left and right arrow keys to move along a slider as needed. Click here to launch the interactive figure. Which of the following points are on the line L? A. \( (-4,2) \) B. \( (1,-5) \) OC. \( (-5,1) \) OD. \( (2,3) \)

To graph the line \( y = 6x - 2 \) using the slope and \( y \)-intercept sliders, set the slope to 6 and the \( y \)-intercept to -2. You then create a parallel line \( L \) through the point \( (2,1) \). Since parallel lines have the same slope, line \( L \) will also have a slope of 6, so its equation can be written as \( y - 1 = 6(x - 2) \), which simplifies to \( y = 6x - 11 \). To find which points lie on the line \( L \), substitute the \( x \)-values of each point into the equation \( y = 6x - 11 \) and check if the resulting \( y \)-value matches the given \( y \)-value. Now, let's substitute and check the points: - A. For \( (-4,2) \): \( y = 6(-4) - 11 = -24 - 11 = -35 \) (not on the line). - B. For \( (1,-5) \): \( y = 6(1) - 11 = 6 - 11 = -5 \) (on the line). - C. For \( (-5,1) \): \( y = 6(-5) - 11 = -30 - 11 = -41 \) (not on the line). - D. For \( (2,3) \): \( y = 6(2) - 11 = 12 - 11 = 1 \) (not on the line). Thus, the point that lies on line \( L \) is B. \( (1,-5) \).