Final answer:
To find the value of y that satisfies the conditions, we need to find the slope of each line and set them equal to each other. Solving for y, we get y = -3.
Step-by-step explanation:
To find the value of y that satisfies the given conditions, we need to determine the slope of the line containing (1, -3) and (3, y), and then find another point on this line.
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula: m = (y2 - y1) / (x2 - x1).
Using this formula, the slope of the line containing (1, -3) and (3, y) is: m1 = (y - (-3))/(3 - 1) = (y + 3)/2.
Since the line is parallel to the line containing (5, -6) and (9, y), their slopes must be equal. The slope of the line containing (5, -6) and (9, y) is: m2 = (y - (-6))/(9 - 5) = (y + 6)/4.
Setting m1 = m2, we get: (y + 3)/2 = (y + 6)/4.
Cross multiplying and simplifying, we have: 2(y + 6) = 4(y + 3). Solving for y, we get: y = -3.
Learn more about Finding the value of y in parallel lines