Question

graph 1
symmetry:
□x - axis
□y - axis
□origin

Explanation:

Step1: Recall symmetry - tests

For x - axis symmetry, replace y with - y in the equation of the line. For y - axis symmetry, replace x with - x. For origin symmetry, replace x with - x and y with - y.

Step2: Analyze the graph visually

The line in the graph does not have x - axis symmetry (if we reflect the line over the x - axis, we get a different line). It does not have y - axis symmetry (if we reflect the line over the y - axis, we get a different line).

Step3: Check origin symmetry

If we rotate the line 180 degrees about the origin, the line coincides with itself. Mathematically, for a linear function \(y = mx + b\), if the line passes through \((x,y)\) and \((-x,-y)\), it has origin symmetry. In this case, the line has origin symmetry.

Answer:

origin