Final answer:
The equation of the line that passes through the point (-7,-6) and is parallel to the line x - y = 5 is y = x + 1. The equation of the line that passes through the point (-7, -6) and is parallel to the line x - y = 5 is y = x + 1.
Step-by-step explanation:
To find an equation of the line that passes through the point (-7,-6) and is parallel to the line x - y = 5, we first need to identify the slope of the given line. By rearranging the given equation into slope-intercept form (y = mx + b), where m is the slope, we get y = x - 5. So, the slope of the given line is 1.
Since parallel lines have the same slope, our new line will also have a slope of 1. Now, we use the point-slope form to create the equation of our new line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Plugging in the point (-7, -6) and the slope 1 gives us y - (-6) = 1(x - (-7)) or y + 6 = x + 7. Simplifying, we get y = x + 1 as the equation of the line.