Answer
Verified
412.2k+ views
Hint: From the coordinates of two points given in the question, which are $\left( -3,-1 \right)$ and $\left( -5,-1 \right)$, we can find the equation of the line passing through them. For this we need to use the two point form of the equation of line which is given as $y-{{y}_{1}}=\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}\left( x-{{x}_{1}} \right)$. From the coordinates given in the question, we can choose ${{x}_{1}}=-3$, ${{y}_{1}}=-1$, ${{x}_{2}}=-5$, ${{y}_{2}}=-1$ and substitute it in the two point equation to get the equation of the line. Then, comparing the obtained equation with the point slope form given by $y=mx+c$ we can determine the required value of the slope.
Complete step by step answer:
Let us label the two points given in the question as A and B so that the coordinates of point A are $\left( -3,-1 \right)$ and that of the point B are $\left( -5,-1 \right)$.
Now, since we are given information about the two points, we can obtain the equation of line from them. This is because we know that the only curve which can be completely described by two points is a line. We have the coordinates of two points, so we apply the two point form to get the equation of the line passing through A and B. The two point form of a line, as we know, is given by
$y-{{y}_{1}}=\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}\left( x-{{x}_{1}} \right)$
Let us take ${{x}_{1}}=-3$, ${{y}_{1}}=-1$, ${{x}_{2}}=-5$, ${{y}_{2}}=-1$ and substitute these in the above equation to get
\[\begin{align}
& \Rightarrow y-\left( -1 \right)=\dfrac{-1-\left( -1 \right)}{-5-\left( -3 \right)}\left( x-\left( -3 \right) \right) \\
& \Rightarrow y+1=\dfrac{-1+1}{-5+3}\left( x+3 \right) \\
& \Rightarrow y+1=\dfrac{0}{-2}\left( x+3 \right) \\
& \Rightarrow y+1=0 \\
\end{align}\]
Subtracting $1$ from both the sides, we get
$\begin{align}
& \Rightarrow y+1-1=0-1 \\
& \Rightarrow y=-1 \\
& \Rightarrow y=\left( 0 \right)x-1 \\
\end{align}$
Comparing the point slope form of the line, which is given by $y=mx+c$, we get \[m=0\] and \[c=-1\].
Hence, the slope is equal to zero.
Note: From the coordinates given in the question, we can observe that the y-coordinate for both the points is the same each being equal to $-1$. Interpreting this information geometrically, we can appreciate that the line passing through both the points will be a horizontal line cutting the y-axis at $\left( 0,-1 \right)$.
Complete step by step answer:
Let us label the two points given in the question as A and B so that the coordinates of point A are $\left( -3,-1 \right)$ and that of the point B are $\left( -5,-1 \right)$.
Now, since we are given information about the two points, we can obtain the equation of line from them. This is because we know that the only curve which can be completely described by two points is a line. We have the coordinates of two points, so we apply the two point form to get the equation of the line passing through A and B. The two point form of a line, as we know, is given by
$y-{{y}_{1}}=\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}\left( x-{{x}_{1}} \right)$
Let us take ${{x}_{1}}=-3$, ${{y}_{1}}=-1$, ${{x}_{2}}=-5$, ${{y}_{2}}=-1$ and substitute these in the above equation to get
\[\begin{align}
& \Rightarrow y-\left( -1 \right)=\dfrac{-1-\left( -1 \right)}{-5-\left( -3 \right)}\left( x-\left( -3 \right) \right) \\
& \Rightarrow y+1=\dfrac{-1+1}{-5+3}\left( x+3 \right) \\
& \Rightarrow y+1=\dfrac{0}{-2}\left( x+3 \right) \\
& \Rightarrow y+1=0 \\
\end{align}\]
Subtracting $1$ from both the sides, we get
$\begin{align}
& \Rightarrow y+1-1=0-1 \\
& \Rightarrow y=-1 \\
& \Rightarrow y=\left( 0 \right)x-1 \\
\end{align}$
Comparing the point slope form of the line, which is given by $y=mx+c$, we get \[m=0\] and \[c=-1\].
Hence, the slope is equal to zero.
Note: From the coordinates given in the question, we can observe that the y-coordinate for both the points is the same each being equal to $-1$. Interpreting this information geometrically, we can appreciate that the line passing through both the points will be a horizontal line cutting the y-axis at $\left( 0,-1 \right)$.
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
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE