Answer
Verified
423k+ views
Hint: The slope is also known as gradient which describes the direction and the steepness of the line. The slope of a line in the plane containing the X and Y axis is generally represented by the letter m, and is defined as the change in the Y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line. Mathematically, it is expressed as following,
\[\begin{align}
&\text{we have two given points }({{x}_{1}},{{y}_{1}})\text{ and }({{x}_{2}},{{y}_{2}})\text{ then slope ''m'' is given by,} \\
&\text{m= }\tan \theta =\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}} \\
\end{align}\]
Here, \[\theta \] is the angle made by the line joining the two given points with the X axis in an anticlockwise direction.
Complete step-by-step answer:
In the given question we have \[{{x}_{1}}=2,{{y}_{1}}=3\text{ and }{{x}_{2}}=4,{{y}_{2}}=7.\]
\[\begin{align}
& \text{we have two given points }({{x}_{1}},{{y}_{1}})\text{ and }({{x}_{2}},{{y}_{2}})\text{ then slope ''m'' is given by,} \\
& \text{m= }\tan \theta =\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}} \\
\end{align}\]
So, the slope “m” is as follow;
\[\begin{align}
& \Rightarrow m=\dfrac{7-3}{4-2} \\
& \Rightarrow m=\dfrac{4}{2}=2 \\
\end{align}\]
Hence, the slope will be equal to 2.
Therefore, the correct answer of the above question is 2.
NOTE: Remember the formula to calculate the slope when two points are given which is also shown below:
We have two given points $({{x}_{1}},{{y}_{1}})\text{ and }({{x}_{2}},{{y}_{2}})$ then the slope “m” is given by,
\[m=\tan \theta =\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}\]
The concept of slope is very important in mathematics as well as in engineering as it applies directly to grades or gradients in geography and civil engineering. Through trigonometry, the slope of the line is related to its angle of incline \[\theta \] by the tangent function which I have mentioned in the solution.
\[\begin{align}
&\text{we have two given points }({{x}_{1}},{{y}_{1}})\text{ and }({{x}_{2}},{{y}_{2}})\text{ then slope ''m'' is given by,} \\
&\text{m= }\tan \theta =\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}} \\
\end{align}\]
Here, \[\theta \] is the angle made by the line joining the two given points with the X axis in an anticlockwise direction.
Complete step-by-step answer:
In the given question we have \[{{x}_{1}}=2,{{y}_{1}}=3\text{ and }{{x}_{2}}=4,{{y}_{2}}=7.\]
\[\begin{align}
& \text{we have two given points }({{x}_{1}},{{y}_{1}})\text{ and }({{x}_{2}},{{y}_{2}})\text{ then slope ''m'' is given by,} \\
& \text{m= }\tan \theta =\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}} \\
\end{align}\]
So, the slope “m” is as follow;
\[\begin{align}
& \Rightarrow m=\dfrac{7-3}{4-2} \\
& \Rightarrow m=\dfrac{4}{2}=2 \\
\end{align}\]
Hence, the slope will be equal to 2.
Therefore, the correct answer of the above question is 2.
NOTE: Remember the formula to calculate the slope when two points are given which is also shown below:
We have two given points $({{x}_{1}},{{y}_{1}})\text{ and }({{x}_{2}},{{y}_{2}})$ then the slope “m” is given by,
\[m=\tan \theta =\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}\]
The concept of slope is very important in mathematics as well as in engineering as it applies directly to grades or gradients in geography and civil engineering. Through trigonometry, the slope of the line is related to its angle of incline \[\theta \] by the tangent function which I have mentioned in the solution.
Recently Updated Pages
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE
Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE
What are the possible quantum number for the last outermost class 11 chemistry CBSE
Is C2 paramagnetic or diamagnetic class 11 chemistry CBSE
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Write an application to the principal requesting five class 10 english CBSE
Difference Between Plant Cell and Animal Cell
a Tabulate the differences in the characteristics of class 12 chemistry CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
Discuss what these phrases mean to you A a yellow wood class 9 english CBSE
List some examples of Rabi and Kharif crops class 8 biology CBSE