Question

which ordered pairs are solutions to the equation? select all that apply. (-2, -3) (6, -4) (4, -1) (0, 6) (-5, 0) (3, 3)

Explanation:

Step1: Recall the definition of a solution to a linear equation's graph

A solution to the equation of a line is an ordered pair \((x, y)\) that lies on the line. So we need to check if each given ordered pair is on the graphed line.

Step2: Check \((-2, -3)\)

Locate \(x = -2\) on the x - axis and then find the corresponding \(y\) - value on the line. When \(x=-2\), looking at the graph, the \(y\) - value of the line at \(x = - 2\) is \(-3\). So \((-2,-3)\) lies on the line.

Step3: Check \((6, - 4)\)

Locate \(x = 6\) on the x - axis. The line at \(x = 6\) has a \(y\) - value. From the graph, when \(x = 6\), the \(y\) - value of the line is not \(-4\) (since the line is increasing and at \(x = 6\), the \(y\) - value should be positive as seen from the graph's trend). So \((6,-4)\) does not lie on the line.

Step4: Check \((4, - 1)\)

Locate \(x = 4\) on the x - axis. The line at \(x = 4\) has a \(y\) - value. From the graph, when \(x = 4\), the \(y\) - value of the line is positive (around \(4\) or \(5\) based on the slope and intercept), not \(-1\). So \((4,-1)\) does not lie on the line.

Step5: Check \((0,6)\)

Locate \(x = 0\) (the y - axis). The line intersects the y - axis at \(y=-1\) (from the graph, the y - intercept is \((0, - 1)\) approximately). So when \(x = 0\), \(y
eq6\), so \((0,6)\) does not lie on the line.

Step6: Check \((-5,0)\)

Locate \(x=-5\) on the x - axis. The line at \(x=-5\) has a \(y\) - value. From the graph, when \(x=-5\), the \(y\) - value of the line is negative (since the line has a positive slope and at \(x = 0\) it's \(-1\), so at \(x=-5\) it should be much more negative), not \(0\). So \((-5,0)\) does not lie on the line.

Step7: Check \((3,3)\)

Locate \(x = 3\) on the x - axis. From the graph, when \(x = 3\), the \(y\) - value of the line is \(3\) (since the line passes through \((3,3)\) as seen from the grid). So \((3,3)\) lies on the line.

Answer:

The correct ordered pairs are \((-2, - 3)\) and \((3,3)\)