Final answer:
The question likely seeks the value of x for a line that passes through (-3,7) and (2,9), and presumably passes through (10,-4) and (x,-6), but there may be a misunderstanding as these sets of points might not be on the same line.
Step-by-step explanation:
The student's question seems to be asking for the value of x for a point that lies on a line which passes through the points (-3,7) and (2,9) and also goes through the points (10,-4) and (x,-6). To find the value of x, we need to determine the equation of the line connecting these points and then solve for x when y is -6. We can find the slope of the line (dependence of y on x) using the original two points and use the slope-intercept form (y=mx+b) to write the equation of the line. However, the provided points (10, -4) and (x, -6) do not necessarily lie on the line defined by (-3,7) and (2,9). So, there could be a misunderstanding in the question as it implies two distinct lines.
If the question is about confirming whether the points (10, -4) and (x, -6) lie on the same line as (-3,7) and (2,9), we would first calculate the slope of the original line and then verify if the other two points match the same slope and equation.