I'm not sure what you mean by "the" linear equation.
"A" linear equation is the equation of a line.
4x+7 = 2x + 5 is a linear equation in 1 variable.
If you were to solve for x, you would get x = -1 which, if graphed, is a vertical line.
For example y = 3x + 7 is a linear equation in two variables. This particular line has a slope of 3 and a y-intercept at (0,7). If graphed, it would pass through the y-axis at (0,7) and "rise" vertically +3 units for each horizontal "run" of +1 unit.
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