Thus the line of zero slope is parallel to the x-axis. This means that either the line is x-axis or it is parallel to the x-axis. Let θ be the angle of inclination of the given line with the positive direction of the x-axis in an anticlockwise sense. What can be said regarding a line is its slope is zero ? Let us now understand the slop using some examples. The angle of inclination of a line with the positive direction of the x-axis in an anticlockwise sense always lies between 0 0 and 180 0. Also, the slope of a line equally inclined with axes is 1 or -1 as it makes an angle of 45 o or 135 o with the x-axis. a line that is perpendicular to the x-axis makes an angle of 90 o with the x-axis, so its slope is tan $\frac$ = ∞. Since a line parallel to the x-axis makes an angle of 0 o with the x-axis, therefore, its slope is tan 0 0 = 0Ī line parallel to the y-axis, i.e.
The slope of a line is generally denoted by m. The trigonometrical tangent of the angle that a line makes with the positive direction of the x-axis in an anticlockwise sense is called the slope or the gradient of a line. To find the gradient of a parallel line, let us first recall what we mean by the slope of a line. It should be noted that the slope of any two parallel lines is always the same. The steepness of the line is determined by the slope or the gradient of the lone which is represented by the value m. The Slope Intercept forms of a straight line is given by y = m x + c, where ‘m’ is the slope and ‘c’ is the y-intercept. Equationįor obtaining the equation of parallel lines, let us recall what we mean by the slope intercept form of the equation of a line. For instance, below we have the lines l and m as intersecting lines as they are not parallel. It should be noted that if two lines are not parallel, they will intersect each other.
Symbolically, two parallel lines l and m are written as l || m. No matter how much we extend the parallel lines in each direction, they would never meet.This means that parallel lines are always the same distance apart from each other. The distance between a pair of parallel lines always remains the same.The following are the properties of parallel lines – Thus we can define parallel lines as – “Two lines l and m in the same plane are said to be parallel lines of they do not intersect when produced indefinitely in either direction.” Properties There can be many lines in a plane, some of which may intersect each other while some may not intersect when produced in either direction. Real Life Applications of Parallel Lines.Rules for Parallel Lines Intersected by a Transversal.Alternate Exterior Angles in a Transversal.But you could always turn that into the form #y=mx+b# to find your slope #m# by simply solving for #y#. Here, you can't directly pick out the slope. Sometimes though, linear equations aren't in the form #y=mx+b#. Note that they have to be different, because if they were equal, then you'd just have two identical lines that technically intersect in every single point. In the general equation of a line #y=mx+b#, the #m# represents your slope value.Īn example of paralell lines would therefore be: So, to find an equation of a line that is parallel to another, you have to make sure both equations have the same slope. Because of this, a pair of parallel lines have to have the same slope, but different intercepts (if they had the same intercepts, they would be identical lines).
Parallel lines are lines that never intersect.
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