Final answer:
To perform composite transformations, apply each transformation in order. For (x, y) → (x, y + 1); y = -x, the new equation will be y = -x + 1. For (x, y) → (x + 3, y + 3); y = x, the new equation will be y = x + 3.
Step-by-step explanation:
To perform each set of composite transformations, we need to apply each transformation in order. Let's start with question 14. The first transformation is (x, y) → (x, y + 1), which means we are shifting the y-coordinate of each point up by 1 unit. The equation y = -x represents a line in the coordinate plane. If we apply the first transformation to this line, it will shift the line up by 1 unit. So the new equation will be y = -x + 1. To graph the final coordinates, we can plot some points on the initial line and then plot the corresponding points on the new line.
For question 15, the first transformation is (x, y) → (x + 3, y + 3), which means we are shifting each point 3 units to the right and 3 units up. The equation y = x represents a line in the coordinate plane. If we apply the first transformation to this line, it will shift the line 3 units to the right and 3 units up. So the new equation will be y = x + 3. To graph the final coordinates, we can plot some points on the initial line and then plot the corresponding points on the new line.