Final answer:
The two lines with different slopes, found using the slope formula (Δy/Δx), are not parallel and do not represent the same line. They are considered intersecting lines since they have unique slopes, however, further information is needed to completely define their relationship.
Step-by-step explanation:
The relationship between the line passing through points (−7, 1) and (−11, 4) and the line passing through points (−9, −3) and (−6, −7) can be determined by calculating the slope of each line. The slope of a line is found using the formula Δy/Δx, which represents the change in y over the change in x, for any two points on the line. Let's calculate the slopes:
- For the first line: slope m1 = (4 − 1)/(−11 − (−7)) = 3/(−11 + 7) = 3/−4 = −0.75
- For the second line: slope m2 = (−7 − −3)/(−6 − (−9)) = −4/3
Since the slopes m1 and m2 are different (m1 = −0.75 and m2 = −4/3), the two lines are not parallel and neither are they the same line. If the slopes were equal, the lines would be parallel. If the lines cross each other at a point, they are considered intersecting lines, but without the exact slope values or graphs presented, we can't definitively determine the full nature of their relationship.