Final answer:
The equation of the line parallel to y = x + 4 and passing through the point (-1, 2) is y = x + 3.
Step-by-step explanation:
The student's question is asking us to work out the equation of a line that is parallel to another line and that passes through a specific point. In this case, the given point is (-1, 2), and the line it must be parallel to is described by the equation y = x + 4. Since parallel lines have the same slope, our new line will have the same slope as this one, which is 1, given that the slope (m) in the line's equation y = mx + b is the coefficient of x.
The general form of an equation for a line is y = mx + b, where m is the slope and b is the y-intercept. Since our line must be parallel to y = x + 4, it will have the same slope, m = 1. To find the y-intercept (b), we substitute the given point into the equation and solve for b:
- y = mx + b
- 2 = (1)(-1) + b
- 2 = -1 + b
- b = 3
Therefore, the equation of our line is y = x + 3.