Final answer:
To find the solution to the system of equations represented by y = -x - 3 and y = x + 1, graph both lines and find their intersection. Upon solving, the intersection is (-2, -1), which is not listed among the given options; hence, the correct answer is D - No solution.
Step-by-step explanation:
When you are asked to graph the equation y = x + 1 on a grid with an existing line representing y = -x - 3, these two equations form a system. To find their point of intersection, which represents the solution to the system of equations, you would graph both lines on the same grid and see where they cross. The equation y = x + 1 is also linear with a slope (m) of 1 and a y-intercept (b) of 1. You can plot this line by starting at the y-intercept (0,1) and using the slope to find another point, for instance (1,2). To solve for the intersection, set the two equations equal to each other:
-x - 3 = x + 1
Combine like terms to get:
-2x = 4
Divide by -2:
x = -2
Plug x back into either equation to solve for y:
y = -2 + 1 = -1
The solution to the system is (-2, -1), which does not match any of the options provided. Thus, the answer is D - No solution.