Answer

Verified

448.2k+ views

**Hint:**The slope of a line in the plane containing the \[x\] and \[y\] axes in generally represented by the letter m, and is defined by as the change in the \[y\]coordinates divided by the corresponding change in the \[x\]coordinate, between two distinct point on the line.

This is described by equation:

\[m = \dfrac{{\mathop y\nolimits_2 - \mathop y\nolimits_1 }}{{\mathop x\nolimits_2 - \mathop x\nolimits_1 }}\]

Where points \[(\mathop x\nolimits_1 ,\mathop y\nolimits_1 )\]and \[(\mathop x\nolimits_2 ,\mathop y\nolimits_2 )\] the change in \[x\] from one to the other is \[\mathop x\nolimits_2 - \mathop x\nolimits_1 \](run). While the change in \[y\] is \[\mathop y\nolimits_2 - \mathop y\nolimits_1 \] (rise) substituting both quantities into the above equation generates the formula.

**Complete step-by- step solution:**

Given, A line run through two points \[P = ( - 2,5)\]\[Q = (6,4)\]

Here in \[P = ( - 2,5)\] represents \[{x_1} , {y_1}\] where \[{x_1} = - 2,{y_1} = 5\]

And also \[Q = (6,4)\] represents \[{x_2} , {y_2}\] where \[{x_2} = 6,{y_2} = 4\]

We know that the slope of line is given by

\[m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\]

Substitute the values \[{x_1} = - 2,{x_2} = 6\,and\,{y_1} = 5,{y_2} = 4\] we get,

\[m(slope) = \dfrac{{4 - 5}}{{6 - ( - 2)}}\]

\[m = \dfrac{{ - 1}}{{6 + 2}}\]

\[m = \dfrac{{ - 1}}{8}\]

Required slope of line \[m = \dfrac{{ - 1}}{8}\]

**Note:**A line is a one-dimensional figure, which has length but no width. A line made of a set of points which is extended in opposite directions infinitely. It is determined by two points in a two-dimensional plane. The two points which lie on the same line are said to be collinear points.

In geometry, there are different types of lines such as horizontal and vertical lines, parallel and perpendicular lines. These lines play an important role in the construction of different types of polygons.

For example, a square is made by four lines of the same lengths, whereas a triangle is made by joining three lines end to end. The above formula fails for a vertical line, parallel to\[y - axis\], where the slope can be taken as infinite. Since the slope is negative, the direction of the line is decreasing.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Which are the Top 10 Largest Countries of the World?

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

How do you graph the function fx 4x class 9 maths CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Change the following sentences into negative and interrogative class 10 english CBSE