Answer
397.5k+ views
Hint: In this question, we are given a linear equation that represents the equation of a line in the x-y plane and we have to find the x and y intercepts of this equation. We can find out the x and y intercepts of the line from its equation. The intercept form of the equation of a line is $\dfrac{x}{a} + \dfrac{y}{b} = 1$ where a is the x-intercept of this line ad b is the y-intercept of the line. We will first convert the given equation into the intercept form and then compare them. The given line is a straight line and all the points lying on the line will satisfy its equation.
Complete step by step solution:
The equation of the line given to us is \[5x + 3y = 15\] .
We will convert this equation into the standard equation of x and y-intercept form as follows –
\[
\dfrac{{5x}}{{15}} + \dfrac{{3y}}{{15}} = 1 \\
\Rightarrow \dfrac{x}{3} + \dfrac{y}{5} = 1 \\
\]
On comparing this equation with the standard equation of x and y-intercept form $\dfrac{x}{a} + \dfrac{y}{b} = 1$ ,
We get –
$a = 3$ and $b = 5$
Hence the x-intercept of the given equation is 3, and the intercept of this equation is 5.
Note: The equation of a line can be written in various ways like slope-intercept form, intercept form etc. the x-intercept of a line is a point on the x-axis at which the line cuts the x-axis and the y-intercept is defined as a point on which the line cuts the y-axis. Thus, we can also find the x and y intercepts by putting the other point equal to zero.
Complete step by step solution:
The equation of the line given to us is \[5x + 3y = 15\] .
We will convert this equation into the standard equation of x and y-intercept form as follows –
\[
\dfrac{{5x}}{{15}} + \dfrac{{3y}}{{15}} = 1 \\
\Rightarrow \dfrac{x}{3} + \dfrac{y}{5} = 1 \\
\]
On comparing this equation with the standard equation of x and y-intercept form $\dfrac{x}{a} + \dfrac{y}{b} = 1$ ,
We get –
$a = 3$ and $b = 5$
Hence the x-intercept of the given equation is 3, and the intercept of this equation is 5.
Note: The equation of a line can be written in various ways like slope-intercept form, intercept form etc. the x-intercept of a line is a point on the x-axis at which the line cuts the x-axis and the y-intercept is defined as a point on which the line cuts the y-axis. Thus, we can also find the x and y intercepts by putting the other point equal to zero.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science 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)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 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)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![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)
How do you graph the function fx 4x class 9 maths 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)