Parallel lines are the lines 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. Basically for any straight line y = mx + b, m is referred to as slope.
Slopes of two parallel lines are equal. If the slope of two parallel lines are $m_1$ and $m_2$ then $m_1$ = $m_2$.
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Let y = m1x + c1 and y = m2x + c2 be two parallel lines then there slopes will be equal.
=> m1 = m2
In the above diagram, we can see the slope of two parallel lines. Both the slopes will have same value. Slope is the 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 or always have the same slope.
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.
Two lines are parallel if they have same slope. The equation of the parallel line in slope-intercept form is y = mx + c, where m is the slope of the line.
If a transversal makes equal intercepts on three or more parallel lines, then any other line cutting them will also make equal intercepts.
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
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
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.
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 is
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 is
m2 = 2.
Since the value of the slopes m1 = m2 = 2 are equal.
Hence, the given lines are parallel.(Answer)
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.
We know that, the slopes of the two parallel lines must be the same.
Hence, the slope of required line is = 5 (Answer)
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