Use the Slope and \( y \)-Intercept sliders to graph the line \( y=-4 x-3 \). Click and drag the red point to \( (4,2) \). Select Perpendicular and check the Show 2nd Line box to graph a line \( L \) through \( (4,2) \). Find the \( x \)-intercept of line L . 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 x-intercept of line L is . (Type an ordered pair.)

To graph the line \( y = -4x - 3 \), you'll see a steep line going downwards with a negative slope. The slope of -4 means for every unit you move right, you move down 4 units, making it quite steep! Now, when you drag the red point to the coordinates \( (4, 2) \), this point sits above the line since the y-value is greater than what the line would predict at that x-value. Next, to find the x-intercept of line L, which is perpendicular to our original line and passes through the point \( (4, 2) \), remember that perpendicular lines have slopes that are negative reciprocals of each other. So, if the slope of our original line is -4, the slope of line L will be \( \frac{1}{4} \). Using point-slope form from point \( (4, 2) \), we can find the equation of line L. Solving for the x-intercept, you’ll discover it crosses the x-axis at the ordered pair \( (6, 0) \).