Slope of Parallel Lines
In this page we are going to learn about slope of a parallel lines concept. Parallel lines are line which does not intersect in any direction. Slope of a line is the value of the angle that a straight line makes with the positive direction of x-axis in the anticlockwise sense. Slope is also refer to as Gradient. Basically for any straight line y = mx + b , m is referred to as slope. The slope of two parallel lines are related in particular way, we will see them below.
Slope of a line in ratio of change in y axis to x axis that is the small change in entity in the y axis to the small change in entity in the x axis is called as slope. Parallel lines are the lines that lie in the same plane have the property that they never intersect each other. They never meet at a point. They are always the same distance apart. Let y = m1x+c1 and y= m2x + c2 be two parallel lines then there slopes will be equal.
In the above diagram we can see the slope of two parallel lines. Both the slopes will have same value. Slope is te ratio of change in y to change in x. When we consider two parallel lines there ratios will be equivalent.
Parallel lines have the value of the angle made with the x axis always same.. they always have the same slope.
Slopes of two parallel lines are equal.
Let the equation of two lines be y=(m1)x + c1 and y=(m2)x + c2 where m1 and m2 are slopes of the lines. The two lines are parallel if and only if m1 = m2.
Here are some examples on slope of parallel lines -
Example1:
Find the equation of a straight line parallel line parallel to y-axis and passing through the point (-3,2).
Solution:
We know that the equation of a straight line parallel to y-axis is
x = a
Since it passes through the point (-3,2), we get -3=a i.e.
a = -3.
Substituting this values of a we get
x = - 3 i.e. x + 3 = 0, which is the required equation.
Example 2 :
Given the equations of two lines 2y - 4x = 12 and y = 2x +8. Check whether the given lines are parallel or not ?
Solution :
The equation of the two lines are given in the question. In order to check that the lines are parallel or not we have to calculate slope. First convert the equation of lines into standard form y = mx+b to identify the slope.
Given the equation of the first line is
2y - 4x = 12.
2y = 4x+12
Dividing both sides by 2 we have
y =2x+ 6.
Hence slope of the first line say
m1 = 2.
Given the equation of the second line is
y=2x + 8. It is already in the standard form.
Hence slope of the second line say
m2 = 2.
Since the value of the slopes m1 = m2 = 2 are equal ,
hence the given lines are parallel.(Answer)
Example 3 :
Given the equation of a line y = 5x +8. What is the slope of the line parallel to given line ?
Solution :
The equation of the line given is y=5x+8 .
It is in the standard form y = mx+b.
Hence slope of the line is 5.
As we have to find the slope of the line parallel to the line y=5x + 8.
Now if the lines are given parallel then the slopes of the two lines must be the same.
Hence the slope of the line = 5 (Answer)
If a transversal makes equal intercepts on three or more parallel lines, then any other line cutting them will also make equal intercepts.
Data:
AP || BQ || CR. The intercepts AB and BC are equal. PQ, QR are the intercepts on any other line.
To Prove Intercept Theorem:
PQ = QR
Construction:
Through A and B draw AE and BF parallel to PQR to cut BQ and CR at E and F respectively.
To prove that PQ = QR
Proof:
