## Precalculus (6th Edition) Blitzer

The slope of a line is the rate of change of its y coordinate with respect to its x coordinate. In other words, it is basically a measure of the steepness of the line. In case of two parallel lines, they have the same steepness. So they must have equal slopes. The slope of parallel line is equal: ${{m}_{1}}={{m}_{2}}$ The converse is also true -- that is, if two lines have the same slope, they must be parallel. Consider the following example: Consider, the equations $y=3x+4\,\,\text{ and }\,\,y=3x-4$ of two non-vertical parallel lines with $y-\text{intercepts}\,\,\,\left( 0,4 \right)\,\text{ and }\,\left( 0,-4 \right)$ respectively. In the above equations $y=3x+4\,\,\text{ and }\,\,y=3x-4$, the slope of the line is the coefficient of x. So, the slope of both lines is $m=3$. From the graph, one can conclude that both lines given by the equations $y=3x+4\,\,\text{ and }\,\,y=3x-4$ are parallel. So they have the same slope, that is $m=3$. Hence, if the lines are parallel, then they have the same slope.