Use the Slope and \( y \)-Intercept sliders to graph the line \( y=-3 x+5 \). Click and drag the red point to \( (-3,1) \). Select Perpendicular and check the Show 2nd Line box to graph a line L perpendicular to the given line passing through the point \( (-3,1) \). 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 will line Lalso pass through? A. \( (-2,2) \) B. \( (3,-4) \) C. \( (6,4) \) D. \( (0,5) \)

To find the equation of line L, which is perpendicular to \( y = -3x + 5 \), we need to determine its slope. The slope of the original line is -3, and the slope of a line perpendicular to it is the negative reciprocal, which is \( \frac{1}{3} \). Now, using the slope-intercept form \( y = mx + b \) and the point \( (-3, 1) \), we can find b: 1. Substitute \( m \) with \( \frac{1}{3} \) and \( x \) and \( y \) with -3 and 1: \( 1 = \frac{1}{3}(-3) + b \) \( 1 = -1 + b \) \( b = 2 \) Thus, the equation for line L is \( y = \frac{1}{3}x + 2 \). Now, we'll check which points from the options fall on this line by plugging their coordinates into the equation. A. For \( (-2, 2) \): \( 2 = \frac{1}{3}(-2) + 2 \) \( 2 = -\frac{2}{3} + 2 \) -- Not valid. B. For \( (3, -4) \): \( -4 = \frac{1}{3}(3) + 2 \) \( -4 = 1 + 2 \) -- Not valid. C. For \( (6, 4) \): \( 4 = \frac{1}{3}(6) + 2 \) \( 4 = 2 + 2 \) -- Valid! D. For \( (0, 5) \): \( 5 = \frac{1}{3}(0) + 2 \) \( 5 = 2 \) -- Not valid. So, line L will also pass through point C, \( (6, 4) \)!