Slope of the Line Joining Two Points

We will discuss here about the slope of the line joining two points.

To find the slope of a non-vertical straight line passing through two given fixed points:

Let P (x\(_{1}\), y\(_{1}\)) and Q (x\(_{2}\), y\(_{2}\)) be the two given points. According to the problem, the straight line PQ is non-vertical x\(_{2}\) ≠ x\(_{1}\).

Required to find, the slope of the line through P and Q.

From P, Q draw perpendiculars PM, QN on x-axis and PL ⊥ NQ. Let θ be the inclination of the line PQ, then ∠LPQ = θ.

From the above diagram, we have

PL = MN = ON - OM = x\(_{2}\) - x\(_{1}\) and

LQ = = NQ - NL = NQ - MP = y\(_{2}\) - y\(_{1}\)

Therefore, the slope of the line PQ = tan θ

                                                  = \(\frac{LQ}{PL}\)

                                                  = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

                           = \(\frac{Difference\, of\, ordinates\,of\, the\, given\, points}{Difference\, of\, their\, abscissae}\)


Hence, the slope (m) of a non-vertical line passing through the points P (x\(_{1}\), y\(_{1}\)) and Q (x\(_{2}\), y\(_{2}\)) is given by

slope = m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

 

1. Find the slope of the line passing through the points M (-2, 3) and N (2, 7).

Solution:

Let M (-2, 3) = (x\(_{1}\), y\(_{1}\)) and N (2, 7) = (x\(_{2}\), y\(_{2}\))

We know that the slope of a straight line passing through two points (x\(_{1}\), y\(_{1}\)) and (x\(_{2}\), y\(_{2}\)) is

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

Therefore, slope of MN = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\) = \(\frac{7 - 3}{2 + 2}\) = \(\frac{4}{4}\) = 1.


2. Find the slope of the line passing through the pairs of points (-4, 0) and origin.

Solution:

We know that the coordinate of the origin is (0, 0)

Let P (-4, 0) = (x\(_{1}\), y\(_{1}\)) and O (0, 0) = (x\(_{2}\), y\(_{2}\))

We know that the slope of a straight line passing through two points (x\(_{1}\), y\(_{1}\)) and (x\(_{2}\), y\(_{2}\)) is

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

Therefore, slope of PO = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

                                 = \(\frac{0 - (0}{0 - (- 4)}\)

                                 = \(\frac{0}{4}\)

                                 = 0.


 Equation of a Straight Line









10th Grade Math

From Intercepts Made by a Straight Line on Axes to HOME


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.



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.



Share this page: What’s this?

Recent Articles

  1. 4th Grade Mental Math on Roman Numerals | Roman Numerals Quiz

    Feb 23, 24 03:55 PM

    In 4th grade mental math on numbers, students can practice different questions on write the Hindu-Arabic numerals, write the Roman Numerals, comparison of roman numerals, addition of roman numerals.

    Read More

  2. 4th Grade Mental Math on Numbers | Mental Math 4th Grade with Answers

    Feb 23, 24 02:24 PM

    4th Grade Mental Math on Numbers
    In 4th grade mental math on numbers, students can practice different questions on numbers in figures, number name, place value, face value, comparison of number and formation of greatest and smallest…

    Read More

  3. Roman Numerals | System of Numbers | Symbol of Roman Numerals |Numbers

    Feb 23, 24 01:28 PM

    List of Roman Numerals Chart
    How to read and write roman numerals? Hundreds of year ago, the Romans had a system of numbers which had only seven symbols. Each symbol had a different value and there was no symbol for 0. The symbol…

    Read More

  4. Worksheet on Roman Numerals |Roman Numerals|Symbols for Roman Numerals

    Feb 22, 24 04:15 PM

    Roman Numbers Table
    Practice the worksheet on roman numerals or numbers. This sheet will encourage the students to practice about the symbols for roman numerals and their values. Write the number for the following: (a) V…

    Read More

  5. Roman Symbols | What are Roman Numbers? | Roman Numeration System

    Feb 22, 24 02:30 PM

    Roman Numbers
    Do we know from where Roman symbols came? In Rome, people wanted to use their own symbols to express various numbers. These symbols, used by Romans, are known as Roman symbols, Romans used only seven…

    Read More