Answer
384.9k+ views
Hint:Change of form of the given equation will give the x-intercept and y-intercept of the line $y=- x+6$. We change it to the form of $\dfrac{x}{p}+\dfrac{y}{q}=1$ to find the x intercept, and y intercept of the line as $p$ and $q$ respectively. then we place the points on the axes and from there we draw the line on the graph.
Complete step by step solution:
We are taking the general equation of line to understand the slope and the intercept form of the line $y=-x+6$. The given equation is in the form of $y=mx+k$. m is the slope of the line. The slope of the line is $-1$.
We have to find the x-intercept, and y-intercept of the line $y=-x+6$.
For this we convert the given equation into the form of $\dfrac{x}{p}+\dfrac{y}{q}=1$. From the form we get that the x intercept, and y intercept of the line will be$p$ and $q$ respectively. The points will be $\left( p,0 \right),\left( 0,q \right)$.
The given equation is $y=-x+6$. Converting into the form of $\dfrac{x}{p}+\dfrac{y}{q}=1$, we get
$\begin{align}
& y=-x+6 \\
& \Rightarrow x+y=6 \\
& \Rightarrow \dfrac{x}{6}+\dfrac{y}{6}=1 \\
\end{align}$
Therefore, the x intercept, and y intercept of the line $y=5x-3$ is 6 and 6 respectively. The axes intersecting points are $\left( 6,0 \right),\left( 0,6 \right)$.
Note: A line parallel to the X-axis does not intersect the X-axis at any finite distance. Hence, we cannot get any finite x-intercept of such a line. Same goes for lines parallel to the Y-axis. In case of slope of a line the range of the slope is 0 to $\infty$
Complete step by step solution:
We are taking the general equation of line to understand the slope and the intercept form of the line $y=-x+6$. The given equation is in the form of $y=mx+k$. m is the slope of the line. The slope of the line is $-1$.
We have to find the x-intercept, and y-intercept of the line $y=-x+6$.
For this we convert the given equation into the form of $\dfrac{x}{p}+\dfrac{y}{q}=1$. From the form we get that the x intercept, and y intercept of the line will be$p$ and $q$ respectively. The points will be $\left( p,0 \right),\left( 0,q \right)$.
The given equation is $y=-x+6$. Converting into the form of $\dfrac{x}{p}+\dfrac{y}{q}=1$, we get
$\begin{align}
& y=-x+6 \\
& \Rightarrow x+y=6 \\
& \Rightarrow \dfrac{x}{6}+\dfrac{y}{6}=1 \\
\end{align}$
Therefore, the x intercept, and y intercept of the line $y=5x-3$ is 6 and 6 respectively. The axes intersecting points are $\left( 6,0 \right),\left( 0,6 \right)$.
![seo images](https://www.vedantu.com/question-sets/ab77a763-0e7f-49e0-977c-f9409690922f8303072231729034345.png)
Note: A line parallel to the X-axis does not intersect the X-axis at any finite distance. Hence, we cannot get any finite x-intercept of such a line. Same goes for lines parallel to the Y-axis. In case of slope of a line the range of the slope is 0 to $\infty$
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)