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. Adding 5-digit Numbers with Regrouping | 5-digit Addition |Addition

    Mar 18, 24 02:31 PM

    Adding 5-digit Numbers with Regrouping
    We will learn adding 5-digit numbers with regrouping. We have learnt the addition of 4-digit numbers with regrouping and now in the same way we will do addition of 5-digit numbers with regrouping. We…

    Read More

  2. Adding 4-digit Numbers with Regrouping | 4-digit Addition |Addition

    Mar 18, 24 12:19 PM

    Adding 4-digit Numbers with Regrouping
    We will learn adding 4-digit numbers with regrouping. Addition of 4-digit numbers can be done in the same way as we do addition of smaller numbers. We first arrange the numbers one below the other in…

    Read More

  3. Worksheet on Adding 4-digit Numbers without Regrouping | Answers |Math

    Mar 16, 24 05:02 PM

    Missing Digits in Addition
    In worksheet on adding 4-digit numbers without regrouping we will solve the addition of 4-digit numbers without regrouping or without carrying, 4-digit vertical addition, arrange in columns and add an…

    Read More

  4. Adding 4-digit Numbers without Regrouping | 4-digit Addition |Addition

    Mar 15, 24 04:52 PM

    Adding 4-digit Numbers without Regrouping
    We will learn adding 4-digit numbers without regrouping. We first arrange the numbers one below the other in place value columns and then add the digits under each column as shown in the following exa…

    Read More

  5. Addition of Three 3-Digit Numbers | With and With out Regrouping |Math

    Mar 15, 24 04:33 PM

    Addition of Three 3-Digit Numbers Without Regrouping
    Without regrouping: Adding three 3-digit numbers is same as adding two 3-digit numbers.

    Read More