Question

Which ordered pairs represent points on the graph of this equation? Select all that apply.
–3x+4y=–6

Answer 1

To determine which ordered pairs represent points on the graph of the equation \(-3x + 4y = -6\), we can substitute the \(x\) and \(y\) values from the ordered pairs into the equation and see if the equation holds true.

Let's rewrite the equation in a more manageable form to solve for \(y\):

\[
4y = 3x - 6
\]

\[
y = \frac{3}{4}x - \frac{3}{2}
\]

Now, consider various ordered pairs \((x, y)\) and substitute each into the equation to check if they satisfy it.

Here are a few examples of ordered pairs to evaluate:

1. \((-2, 0)\):
\[
-3(-2) + 4(0) = 6 + 0 = 6 \quad \text{(not equal to -6)}
\]

2. \((0, -1.5)\):
\[
-3(0) + 4(-1.5) = 0 - 6 = -6 \quad \text{(equals -6)}
\]

3. \((2, 0)\):
\[
-3(2) + 4(0) = -6 + 0 = -6 \quad \text{(equals -6)}
\]

4. \((0, -2)\):
\[
-3(0) + 4(-2) = 0 - 8 = -8 \quad \text{(not equal to -6)}
\]

5. \((4, 6)\):
\[
-3(4) + 4(6) = -12 + 24 = 12 \quad \text{(not equal to -6)}
\]

After evaluating a number of pairs, you can continue testing potential ordered pairs in this way until you find all pairs that satisfy the equation.

Feel free to provide a specific list of points if you need further assistance checking them!