Question

Find the value of y that satisfies the given conditions. Then graph the line on a separate sheet of paper. The line containing (1, -3) and (3, y) is parallel to the line containing (5, -6) and (9, y).

Answer 1

The value of y that satisfies the conditions is y = 0.

Explanation:

To find the value of y that satisfies the given conditions, we can first determine the slope of the line containing points (5, -6) and (9, y), and then use that slope to find the value of y for the line containing points (1, -3) and (3, y).

The formula for calculating the slope (m) between two points (x1, y1) and (x2, y2) is:

m = (y2 - y1) / (x2 - x1)

For the line containing points (5, -6) and (9, y):

m = (y - (-6)) / (9 - 5)

Now, the line containing points (1, -3) and (3, y) is parallel, which means it has the same slope as the first line:

m = (y - (-3)) / (3 - 1)

Now, equate these two equations:

(y + 6) / 4 = (y + 3) / 2

To solve for y, cross-multiply:

2(y + 6) = 4(y + 3)

Now, expand and solve for y:

2y + 12 = 4y + 12

Subtract 2y from both sides:

12 = 2y + 12 - 2y

Now, subtract 12 from both sides:

0 = 2y

Divide by 2:

0 / 2 = 2y / 2

y = 0

So, the value of y that satisfies the conditions is y = 0.

Now, you can graph the line containing points (1, -3) and (3, 0) on a separate sheet of paper. The line will be a horizontal line passing through y = 0.

solved by MG