A line passes through the point (0,4) and has a slope of -2. Determine the coordinates of its x-intercept.

To find the x-intercept of the line, we can use the slope-intercept form of a line, which is \(y = mx + b\). Given the slope \(m = -2\) and the point (0,4) where the line crosses the y-axis (which is also the y-intercept \(b\)), we can write the equation as: \[ y = -2x + 4. \] To find the x-intercept, we set \(y = 0\): \[ 0 = -2x + 4. \] \[ 2x = 4. \] \[ x = 2. \] Thus, the coordinates of the x-intercept are \((2, 0)\). Now go ahead and visualize this scenario! Imagine drawing a line starting at point (0,4) and heading downwards due to the negative slope. It's like a slide at the playground—perfect for a quick descent! As it crosses the x-axis, you can peek at the coordinates: voilà, (2, 0) is where the fun ends!