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Answer:
The slope is -1.
Step-by-step explanation:
We want to find the slope of the line that is parallel to the line joining the points (7, -5) and (-5, 7).
First, we can use the slope formula to find the line passing through (7, -5) and (-5, 7). The slope formula is:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute and evaluate:
[tex]\displaystyle m=\frac{(7)-(-5)}{(-5)-(7)}=\frac{12}{-12}=-1[/tex]
So, its slope is -1.
Recall that parallel lines have the same slope.
Therefore, the slope of the line that is parallel to the line joining the points (7, -5) and (-5, 7) will also be -1.