Final answer:
The equation of the line in slope-intercept form that passes through the point (9,-2) and is parallel to the line represented by y = -x + 5 is y = -x + 7.
Step-by-step explanation:
To find the equation of a line that is parallel to a given line, we need to use the fact that parallel lines have the same slope. The slope-intercept form is represented by y = mx + b, where m is the slope and b is the y-intercept. In the given line, the slope is -1. Since our new line is parallel, it will also have a slope of -1. We can now plug in the point (9,-2) into the slope-intercept form and solve for the y-intercept:
-2 = -1(9) + b
b = -2 + 9
b = 7
So, the equation of the line in slope-intercept form that passes through the point (9,-2) and is parallel to the given line is y = -x + 7.
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