Write the point-slope form of the line that passes through (1, -5) and is parallel to a line with a slope of 1. Include all of your work in your final answer. Type your answer in the box provided to submit your solution.
To find the equation of a line parallel to a given line, we need to use the same slope. Given that the line we are looking for is parallel to a line with a slope of 1, we can use that slope in our equation.
The point-slope form of a line is given by:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line, and m is the slope of the line.
We are given the point (1, -5) on the line, so the equation becomes:
y - (-5) = 1(x - 1)
Simplifying the equation:
y + 5 = x - 1
Subtracting 5 from both sides to isolate y:
y = x - 6
So, the point-slope form of the line that passes through (1, -5) and is parallel to a line with a slope of 1 is:
y = x - 6