The y axis represents the vertical co-ordinates whereas the x axis represents the horizontal co-ordinates.
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Yes, x = -3 would represent a vertical line at abscissa -3, parallel to the y-axis.
A cartesian graph is a graph in which y is some function of x. This is the 'normal' type in which you can give an x and y coordinate. Other types include polar in which modulus is a function of argument, but there are loads of varieties and forms.
Tables and graph represent relations by showing the distribution of occurrence.
A graph about masses and volumes would represent density.
b is the variable for the y-intercept, or how far up or down the graph is shifted.