Question

Does the point (-2, 2) lie on the line 2y + 3x = -2? What are the three ways that can help us to determine this?

A) Yes; Graphical method, substitution method, and solving for y.
B) No; Substitution method, addition method, and solving for x.
C) Yes; Addition method, solving for y, and solving for x.
D) No; Graphical method, addition method, and solving for y.

Answer 1

The point (-2, 2) lies on the line 2y + 3x = -2. We can confirm this using the substitution method, and methods like the graphical method and solving for y also help in such determinations. Answer A (Yes) is correct as the equation holds true when values of the given point are substituted.

Step-by-step explanation:

To determine whether the point (-2, 2) lies on the line represented by the equation 2y + 3x = -2, we can use several methods:

1. Substitution method: Substitute the x and y values of the point into the equation and check if the equation holds true.
2. Graphical method: Plot the line and see if the point lies on it. For the given equation, you would need to first express y in terms of x or vice versa, and then plot the line on a graph.
3. Solving for y: Rearrange the given equation to solve for y in terms of x, and then compare the y value from the point (-2, 2) to the computed value when x = -2.

Now, we can use the substitution method to check if the point (-2, 2) lies on the line. Plugging in the values:

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

Since the equation holds true, the point (-2, 2) does indeed lie on the line. Therefore, the correct answer is A: Yes; Graphical method, substitution method, and solving for y.