Question

this is the graph of the equation $y = \frac{6}{5}x$.
which ordered pairs are solutions to the equation? select all that apply.

Explanation:

Since the specific ordered pairs to choose from are not provided, we can explain the general method to determine if an ordered pair \((x,y)\) is a solution to the equation \(y = \frac{6}{5}x\):

Step 1: Recall the definition of a solution to a linear equation

An ordered pair \((x,y)\) is a solution to the equation \(y=\frac{6}{5}x\) if when we substitute the value of \(x\) into the right - hand side of the equation and simplify, we get the value of \(y\) in the ordered pair. Mathematically, for an ordered pair \((x_0,y_0)\), we need to check if \(y_0=\frac{6}{5}x_0\).

Step 2: Example calculation

Suppose we have an ordered pair \((5,6)\). Substitute \(x = 5\) into the equation \(y=\frac{6}{5}x\). Then \(y=\frac{6}{5}\times5=6\), which is equal to the \(y\) - value in the ordered pair \((5,6)\). So \((5,6)\) is a solution.

Suppose we have an ordered pair \((- 5,-6)\). Substitute \(x=-5\) into the equation \(y = \frac{6}{5}x\). Then \(y=\frac{6}{5}\times(-5)=-6\), which is equal to the \(y\) - value in the ordered pair \((-5,-6)\). So \((-5,-6)\) is a solution.

Suppose we have an ordered pair \((10,12)\). Substitute \(x = 10\) into the equation \(y=\frac{6}{5}x\). Then \(y=\frac{6}{5}\times10 = 12\), which is equal to the \(y\) - value in the ordered pair \((10,12)\). So \((10,12)\) is a solution.

If you provide the list of ordered pairs, we can check each of them one by one using the above method.

Answer:

Since the specific ordered pairs to choose from are not provided, we can explain the general method to determine if an ordered pair \((x,y)\) is a solution to the equation \(y = \frac{6}{5}x\):

Step 1: Recall the definition of a solution to a linear equation

An ordered pair \((x,y)\) is a solution to the equation \(y=\frac{6}{5}x\) if when we substitute the value of \(x\) into the right - hand side of the equation and simplify, we get the value of \(y\) in the ordered pair. Mathematically, for an ordered pair \((x_0,y_0)\), we need to check if \(y_0=\frac{6}{5}x_0\).

Step 2: Example calculation

Suppose we have an ordered pair \((5,6)\). Substitute \(x = 5\) into the equation \(y=\frac{6}{5}x\). Then \(y=\frac{6}{5}\times5=6\), which is equal to the \(y\) - value in the ordered pair \((5,6)\). So \((5,6)\) is a solution.

Suppose we have an ordered pair \((- 5,-6)\). Substitute \(x=-5\) into the equation \(y = \frac{6}{5}x\). Then \(y=\frac{6}{5}\times(-5)=-6\), which is equal to the \(y\) - value in the ordered pair \((-5,-6)\). So \((-5,-6)\) is a solution.

Suppose we have an ordered pair \((10,12)\). Substitute \(x = 10\) into the equation \(y=\frac{6}{5}x\). Then \(y=\frac{6}{5}\times10 = 12\), which is equal to the \(y\) - value in the ordered pair \((10,12)\). So \((10,12)\) is a solution.

If you provide the list of ordered pairs, we can check each of them one by one using the above method.