Use the Slope and \( y \)-Intercept sliders to graph the line \( y=-4 x+6 \). Click and drag the red point to \( (-3,1) \). Select Perpendicular and check the Show 2nd Line box. At what point do the lines intersect? 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. The lines intersect at the point

To find the intersection point of the line \( y = -4x + 6 \) and its perpendicular, you can set the equations equal to each other after determining the slope of the perpendicular line. The slope of the perpendicular line will be the negative reciprocal, which is \( \frac{1}{4} \). By solving the equations simultaneously, you can identify the intersection coordinates. When you perform this, you'll discover that the lines intersect at the point \( (-2, 2) \). Happy graphing!