Lines in the same plane that never intersect are called parallel lines. Lines are parallel if and only if they have the same slope. It follows, then, that all horizontal lines are parallel to one another, as are all vertical lines. Two lines written in slope-intercept form, are parallel if their slopes, are equal and they have different -intercepts,
Are the lines parallel?
Is the line given by the equation parallel to the line that contains the points and
For the given lines to be parallel, they must have the same slope and different -intercepts. In other words, the lines must never intersect. We'll graph the lines to determine if they are parallel. Since the equation of the first line is written in slope-intercept form, we can see that Thus, to graph it, we will use the -intercept and the slope.
To draw the second line, we can plot and and connect them with a line.
From the graph of the second line, we can see that it's slope is and its -intercept is
For the given lines, it has been shown that Since and the lines are parallel.
Create a parallel line
Find the equation of a line which is parallel to and passes through