Y = mX + b
m = the slope of the line
b = the number where the line crosses the y-axis
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What you're referring to is called a Linear function. It always looks like y = mx +b when in standard form. Where M is the slope of your line (how tilted is it) and B is where the line crosses the y-axis on the graph. (y-intercept)
The standard expression for a straight line graph is y = ax + b
It is a more complicated mathematical expression.
Yes, a mathematical expression can have no variables, but such an expression is usually not very useful. An example of a valid expression without variables is: 1+1=2
Without an equality sign the given expression can't be considered to be a straight line equation.