# Find out the intersection points of the line $3x + 2y = 6$ with x and y axis respectively.

$

(a){\text{ }}\left( { - 2,0} \right){\text{ and }}\left( {0,3} \right) \\

(b){\text{ }}\left( {2,0} \right){\text{ and }}\left( {0, - 3} \right) \\

(c){\text{ }}\left( {0,2} \right){\text{ and }}\left( {3,0} \right) \\

(d){\text{ }}\left( {2,0} \right){\text{ and }}\left( {0,3} \right) \\

$

Last updated date: 15th Mar 2023

•

Total views: 304.5k

•

Views today: 6.84k

Answer

Verified

304.5k+ views

Hint – In this question we have to find the point of intersection of the given line with x axis and y axis. A line cuts x axis at any point (x, 0) as the y-coordinate on x-axis is 0 similarly a line cuts the y-axis at the point (0, y) as the x-coordinate on y-axis is zero. So use this concept to get the point of intersection.

“Complete step-by-step answer:”

Given equation of the line is

$3x + 2y = 6$

Now we have to find out the intersection points of this line with the axis.

Case 1 – Intersection point with x-axis.

As we know on x-axis the value of y is zero.

So, substitute y = 0 in the given equation we have,

$ \Rightarrow 3x + 2 \times 0 = 6$

Now simplify this equation we have,

$

\Rightarrow 3x = 6 \\

\Rightarrow x = \dfrac{6}{3} = 2 \\

$

So, the intersection point with the x-axis is (2, 0) as shown in figure.

Case 2 – Intersection point with y-axis.

As we know on y-axis the value of x is zero.

So, substitute x = 0 in the given equation we have,

$ \Rightarrow 3 \times 0 + 2y = 6$

Now simplify this equation we have,

$

\Rightarrow 2y = 6 \\

\Rightarrow y = \dfrac{6}{2} = 3 \\

$

So, the intersection point with the y-axis is (0, 3) as shown in figure.

So intersection points of the line with the axis are (2, 0) and (0, 3) as shown in figure.

Hence option (d) is correct.

Note –Whenever we face such types of questions the key concept involved is to have a diagrammatic representation of the line given in question, then using the concept that at the point of intersection with any axis or even with any other line the points must satisfy the equation of line. This will help you get on the right track to reach the answer.

“Complete step-by-step answer:”

Given equation of the line is

$3x + 2y = 6$

Now we have to find out the intersection points of this line with the axis.

Case 1 – Intersection point with x-axis.

As we know on x-axis the value of y is zero.

So, substitute y = 0 in the given equation we have,

$ \Rightarrow 3x + 2 \times 0 = 6$

Now simplify this equation we have,

$

\Rightarrow 3x = 6 \\

\Rightarrow x = \dfrac{6}{3} = 2 \\

$

So, the intersection point with the x-axis is (2, 0) as shown in figure.

Case 2 – Intersection point with y-axis.

As we know on y-axis the value of x is zero.

So, substitute x = 0 in the given equation we have,

$ \Rightarrow 3 \times 0 + 2y = 6$

Now simplify this equation we have,

$

\Rightarrow 2y = 6 \\

\Rightarrow y = \dfrac{6}{2} = 3 \\

$

So, the intersection point with the y-axis is (0, 3) as shown in figure.

So intersection points of the line with the axis are (2, 0) and (0, 3) as shown in figure.

Hence option (d) is correct.

Note –Whenever we face such types of questions the key concept involved is to have a diagrammatic representation of the line given in question, then using the concept that at the point of intersection with any axis or even with any other line the points must satisfy the equation of line. This will help you get on the right track to reach the answer.

Recently Updated Pages

If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE