The side parallel to s is side q. Its endpoints are Point 1 (x1,y1) = 3,6 and Point 2 (x2,y2) = 6,3.
Let's determine the equation of side q.
Step 1: Determining the slope (m).
[tex]\text{ Slope = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\text{ = }\frac{\text{ 6 - 3}}{\text{ 3 - 6}}[/tex][tex]\text{ = }\frac{\text{ 3}}{\text{ -3}}[/tex][tex]\text{ Slope = -1}[/tex]
Step 2: Let's determine the y-intercept (b). Substitute x,y = 3,6 and m = -1 in y = mx + b.
[tex]\text{ y = mx + b}[/tex][tex]\text{ 6 = (-1)(3) + b}[/tex][tex]\text{ 6 = -3 + b}[/tex][tex]\text{ 6 + 3 = b}[/tex][tex]\text{ 9 = b}[/tex]
Step 3: Complete the equation. Substitute m = -1 and b = 9 in y = mx + b.
[tex]\text{ y = mx + b}[/tex][tex]\text{ y = (-1)x + (9)}[/tex][tex]\text{ y = -x + 9}[/tex]
Therefore, the answer is letter A : y = -x + 9
