Question

Which ordered pairs represent points on the graph of this equation?
7x+4y=14

Answer 1

To determine which ordered pairs \((x, y)\) represent points on the graph of the equation \(7x + 4y = 14\), we can substitute the values of \(x\) and calculate the corresponding \(y\) values, or vice versa.

Let's check a few values for \(x\):

1. **When \(x = 0\)**:
\[
7(0) + 4y = 14 \implies 4y = 14 \implies y = \frac{14}{4} = 3.5
\]
The ordered pair is \((0, 3.5)\).

2. **When \(x = 2\)**:
\[
7(2) + 4y = 14 \implies 14 + 4y = 14 \implies 4y = 0 \implies y = 0
\]
The ordered pair is \((2, 0)\).

3. **When \(x = 1\)**:
\[
7(1) + 4y = 14 \implies 7 + 4y = 14 \implies 4y = 7 \implies y = \frac{7}{4} = 1.75
\]
The ordered pair is \((1, 1.75)\).

4. **When \(x = -1\)**:
\[
7(-1) + 4y = 14 \implies -7 + 4y = 14 \implies 4y = 21 \implies y = \frac{21}{4} = 5.25
\]
The ordered pair is \((-1, 5.25)\).

By finding various values, we can generate several ordered pairs. Points like \((0, 3.5)\), \((2, 0)\), \((1, 1.75)\), and \((-1, 5.25)\) all satisfy the equation \(7x + 4y = 14\).

If you have specific ordered pairs you would like me to check against the equation, please provide them!