Condition of Parallelism

We will discuss here about the condition of parallelism.

If two lines are parallel then they are inclined at the same angle θ with the positive direction of the x-axis. So, their slopes are equal.

Two lines with slopes m\(_{1}\) and m\(_{2}\) are parallel if and only if m\(_{1}\) = m\(_{2}\)

Note: If the slope of a line is m then any line parallel to it will also have the slope m.


Solved examples on condition of parallelism:

1. Prove that the lines 3x – 2y – 1 = 0 and 9x - 6y + 5 = 0 are parallel.

Solution:

The slope of the lines can be found by comparing the equations with y = mx + c.

Equation of the first straight line 3x – 2y – 1 = 0

Now we need to express the given equation in the form y = mx + c.

3x – 2y – 1 = 0

-2y = -3x + 1

y = \(\frac{-3}{-2}\)x + \(\frac{1}{-2}\)

y = \(\frac{3}{2}\)x - \(\frac{1}{2}\)

Therefore, the slope (m\(_{1}\)) of the given line = \(\frac{3}{2}\)

Equation of the second line 9x - 6y + 5 = 0

Now we need to express the given equation in the form y = mx + c.

9x - 6y + 5 = 0

-6y = -9x - 5

y = \(\frac{-9}{-6}\)x - \(\frac{5}{-6}\)

y = \(\frac{3}{2}\)x + \(\frac{5}{6}\)

Therefore, the slope (m\(_{2}\)) of the given line = \(\frac{3}{2}\)

Now we can clearly see that the slope of the first line m\(_{1}\) = the slope of the second line m\(_{2}\)

Therefore, the given two lines are parallel.


2. Find the value of k if the lines 7y = kx + 4 and x + 2y = 3 are parallel.

Solution:

The slope of the lines can be found by comparing the equations with y = mx + c.

Equation of the first straight line 7y = kx + 4

Now we need to express the given equation in the form y = mx + c.

7y = kx + 4

y = \(\frac{k}{7}\)x + \(\frac{4}{7}\)

Therefore, the slope (m\(_{1}\)) of the given line = \(\frac{k}{7}\)

Equation of the second line x + 2y = 3

Now we need to express the given equation in the form y = mx + c.

x + 2y = 3

2y = -x + 3

y = -\(\frac{1}{2}\)x + \(\frac{3}{2}\)

Therefore, the slope (m\(_{2}\)) of the given line = -\(\frac{1}{2}\)

Now according o the problem the two given lines are parallel.

i.e., m\(_{1}\) = m\(_{2}\)

\(\frac{k}{7}\) = -\(\frac{1}{2}\)

k = -\(\frac{7}{2}\)

Therefore, the value of k = -\(\frac{7}{2}\)

 Equation of a Straight Line







10th Grade Math

From Condition of Parallelism to HOME




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Share this page: What’s this?

Recent Articles

  1. Worksheet on Word Problems on Fractions | Fraction Word Problems | Ans

    Jul 16, 24 02:20 AM

    In worksheet on word problems on fractions we will solve different types of word problems on multiplication of fractions, word problems on division of fractions etc... 1. How many one-fifths

    Read More

  2. Word Problems on Fraction | Math Fraction Word Problems |Fraction Math

    Jul 16, 24 01:36 AM

    In word problems on fraction we will solve different types of problems on multiplication of fractional numbers and division of fractional numbers.

    Read More

  3. Worksheet on Add and Subtract Fractions | Word Problems | Fractions

    Jul 16, 24 12:17 AM

    Worksheet on Add and Subtract Fractions
    Recall the topic carefully and practice the questions given in the math worksheet on add and subtract fractions. The question mainly covers addition with the help of a fraction number line, subtractio…

    Read More

  4. Comparison of Like Fractions | Comparing Fractions | Like Fractions

    Jul 15, 24 03:22 PM

    Comparison of Like Fractions
    Any two like fractions can be compared by comparing their numerators. The fraction with larger numerator is greater than the fraction with smaller numerator, for example \(\frac{7}{13}\) > \(\frac{2…

    Read More

  5. Worksheet on Reducing Fraction | Simplifying Fractions | Lowest Form

    Jul 15, 24 03:17 PM

    Worksheet on Reducing Fraction
    Practice the questions given in the math worksheet on reducing fraction to the lowest terms by using division. Fractional numbers are given in the questions to reduce to its lowest term.

    Read More