Question

which ordered pairs represent points on the graph of this equation? select all that apply.
$4x - 3y = 5$
$(-3, -4)$ $(-1, -3)$ $(5, 5)$
$(-5, 3)$ $(0, 6)$ $(6, 1)$

Explanation:

To determine if an ordered pair \((x, y)\) is on the graph of the equation \(4x - 3y = 5\), we substitute the values of \(x\) and \(y\) into the equation and check if the left - hand side equals the right - hand side (which is 5).

Step 1: Check the ordered pair \((-3,-4)\)

Substitute \(x=-3\) and \(y = - 4\) into the left - hand side of the equation \(4x-3y\):
\[

$$\begin{align*} 4\times(-3)-3\times(-4)&=-12 + 12\\ &=0 eq5 \end{align*}$$

\]
So, \((-3,-4)\) is not on the graph.

Step 2: Check the ordered pair \((-1,-3)\)

Substitute \(x = - 1\) and \(y=-3\) into the left - hand side of the equation \(4x-3y\):
\[

$$\begin{align*} 4\times(-1)-3\times(-3)&=-4 + 9\\ &=5 \end{align*}$$

\]
Since the left - hand side equals the right - hand side, \((-1,-3)\) is on the graph.

Step 3: Check the ordered pair \((5,5)\)

Substitute \(x = 5\) and \(y = 5\) into the left - hand side of the equation \(4x-3y\):
\[

$$\begin{align*} 4\times5-3\times5&=20 - 15\\ &=5 \end{align*}$$

\]
Since the left - hand side equals the right - hand side, \((5,5)\) is on the graph.

Step 4: Check the ordered pair \((-5,3)\)

Substitute \(x=-5\) and \(y = 3\) into the left - hand side of the equation \(4x-3y\):
\[

$$\begin{align*} 4\times(-5)-3\times3&=-20-9\\ &=-29 eq5 \end{align*}$$

\]
So, \((-5,3)\) is not on the graph.

Step 5: Check the ordered pair \((0,6)\)

Substitute \(x = 0\) and \(y = 6\) into the left - hand side of the equation \(4x-3y\):
\[

$$\begin{align*} 4\times0-3\times6&=0 - 18\\ &=-18 eq5 \end{align*}$$

\]
So, \((0,6)\) is not on the graph.

Step 6: Check the ordered pair \((6,1)\)

Substitute \(x = 6\) and \(y = 1\) into the left - hand side of the equation \(4x-3y\):
\[

$$\begin{align*} 4\times6-3\times1&=24 - 3\\ &=21 eq5 \end{align*}$$

\]
So, \((6,1)\) is not on the graph.

Answer:

The ordered pairs that represent points on the graph of the equation \(4x - 3y=5\) are \((-1,-3)\) and \((5,5)\) (i.e., B. \((-1, - 3)\), C. \((5, 5)\))