What does a reflection across y=x mean? will give brainliest to the person who best explains it.

If you were to graph y=x it would look like if you took the x axis and rotated it 45 degrees counterclockwise with the center of rotation on the origin

basically, it switches x and y
a reflection is like a miror

a reflection across y=x in equation would be

y=3x^2+5x-2 reflected across the y=x axis (aka the identity line) would be
x=3y^2+5y-2

This means that if you graph the point and the line, you have to find a point that is on the other Side of the line that reflects the first point. The line y=x goes through the points (1,1)(2,2)(3,3)... And so forth. Also (-1,-1)(-2,-2) and so on. Draw this line on a coordinate plane. Then plot the point. With a y=x line the reflection must be (x,y) to (y,x). The points are switched. So (4,-2)'s image would be (-2,4). Plot that point. But since the problem does not specifically say graph, you don't have to.