Based on the description you provided, we can analyze the characteristics of the two lines:
- Line K (the orange line) passes through the origin (0,0).
- Line L (the blue dotted line) passes through (-8,0) and (0,8).
From the points given, we can determine the slopes of the lines:
- Line K: Without specific points, we can't ascertain the slope directly from the origin, but we can assume it has some slope from your description.
- Line L: It goes from (-8,0) to (0,8). The slope can be calculated as: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8 - 0}{0 - (-8)} = \frac{8}{8} = 1 \] So, line L has a slope of 1.
If line K has a different slope, we can further analyze the options:
- Line L has been moved up 8 units on the y-axis from Line K - This would not describe their relationship correctly.
- Line L has the opposite slope of Line K - If Line K has a slope of -1, then this could be true if it's a downward slope.
- Line L has been moved 8 units to the right on the x-axis from Line K - This does not seem correct based on the lines' descriptions.
- Line K has a steeper slope than Line L - This could be true if Line K's slope is greater than 1 or less than -1 (for downward).
Based on the potential slopes that could exist, you would need to determine the correct relationship. The most likely correct option among these statements would likely be "Line L has the opposite slope of Line K," assuming line K has a negative slope of -1 (which is typical for a line going down to the right). However, if line K is actually steeper, that option could be more valid.
Select the response that you believe fits best based on the lines' properties observed in the image or described. If you're unsure about the slopes, I'd recommend choosing "Line L has the opposite slope of Line K" if you know Line K is steeply negative relative to line L's positive slope.