Final answer:
The equation of the line that passes through (-2,5) and is parallel to the line y = x + 1 is y = x + 7, as parallel lines have the same slope, which in this case is 1.
Step-by-step explanation:
To write an equation of a line that is parallel to another line, you need to ensure that both lines have the same slope. In this case, the given line is y = x + 1, so the slope (m) is 1 since the coefficient of x is 1. A parallel line will have the same slope.
Using the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope, we can plug in the slope and the given point (-2, 5). This gives us the equation:
y - 5 = 1(x + 2)
Simplifying this equation, we get:
y - 5 = x + 2
And then adding 5 to both sides:
y = x + 7
This is the equation of the line that passes through (-2, 5) and is parallel to y = x + 1.