Question

Here is your ordered pair plotted as a point, together with the linear equation y=x+2(If you can't see your point, maybe you didn't type it correctly, or maybe it's outside the graph window.)Is your ordered pair correct? How do you know?

Answer 1

To determine if an ordered pair is correct in relation to the linear equation \( y = x + 2 \), you need to check if the coordinates of the point satisfy the equation.

An ordered pair is usually represented as \( (x, y) \). To verify if this pair is on the line defined by the equation \( y = x + 2 \):

1. **Substitute** the x-value of your ordered pair into the equation.
2. **Calculate** the expected y-value using the equation.
3. **Compare** this calculated y-value to the y-value in your ordered pair.

For example, if your ordered pair is \( (1, 3) \):

1. Substitute \( x = 1 \) into the equation:
\[
y = 1 + 2 = 3
\]
2. The calculated y-value is \( 3 \), which matches the y-value of the ordered pair \( (1, 3) \).

This means that the ordered pair \( (1, 3) \) is indeed correct, as it lies on the line defined by the equation.

If the ordered pair you have differs from this process (for example, \( (1, 4) \) would yield \( y = 1 + 2 = 3 \), which does not match \( 4 \)), it would indicate that the ordered pair is not correct for the equation \( y = x + 2 \).

You can follow this same process for whatever ordered pair you have to determine its validity in relation to the linear equation.