Question

The points (3, 6) and (5, 12) lie on the graph of a linear equation. Determine whether each of the following points is a solution of the same linear equation. Yes No (4, 8) Yes – (4, 8) No – (4, 8) (0, -3) Yes – (0, -3) No – (0, -3) (2, 2) Yes – (2, 2) No – (2, 2)

Answer 1

The linear equation, derived from the points (3, 6) and (5, 12), is y = 3x - 3. Among the given points, only (0, -3) satisfies the equation, making it the correct solution.

To determine whether a point is a solution to the same linear equation, we can use the slope-intercept form of a linear equation, which is given by:

y = mx + b

where m is the slope and b is the y-intercept.

First, calculate the slope using the given points (3, 6) and (5, 12):

`\[ m = \frac{{12 - 6}}{{5 - 3}} = (6)/(2) = 3 \]`

Now, use the slope-intercept form with one of the points to find the y-intercept (b):

6 = 3(3) + b

6 = 9 + b

b = -3

So, the linear equation is y = 3x - 3.

Now, check each given point:

1. For (4, 8):

8 = 3(4) - 3

8 = 12 - 3

8 = 9 (False)

2. For (0, -3):

-3 = 3(0) - 3

-3 = -3 (True)

3. For (2, 2):

2 = 3(2) - 3

2 = 6 - 3

2 = 3 (False)

Therefore, the correct answer is (0, -3) only.