Question

For the equation 3x+2y+6=0 find the intersecting points by coordinate axes​

Answer 1

Answer:

change into standard form

X/a+Ylb=1

(a,0) and (0, b) are points by coordinate axes

3x+2y+6=0

3x+2y=-6

Divide both sides with -6

3x/-6+2y/-6=-6/-6

x/-2+y/-3=1

so intersecting points by coordinate axis

(-2, 0) and (0 , -3)

Answer 2

SOLUTION

TO DETERMINE

The intersecting points by coordinate axes for the line

$\sf{3x + 2y + 6 = 0 \: \: }$

EVALUATION

Here the equation of the given line is

$\sf{3x + 2y + 6 = 0 \: \: .....(1)}$

PROCESS : 1

We write equation of the line (1) in intercept form as below

$\sf{3x + 2y + 6 = 0 \: \: }$

$\sf{ \implies \: 3x + 2y = - 6 \: \: }$

$\displaystyle \sf{ \implies \frac{3x}{ - 6} + \frac{2y}{ - 6} = 1}$

$\displaystyle \sf{ \implies \frac{x}{ - 2} + \frac{y}{ - 3} = 1}$

This state that the line given by Equation (1) intersects x axis at A(-2,0) and y axis at B (0,-3) respectively

PROCESS : 2

Suppose the line given by Equation (1) intersects x axis at A and y axis at B respectively

Then for the point A , ordinate = 0

From Equation (1) we get

$\implies \sf{3x = - 6}$

$\implies \sf{x = - 2}$

So the coordinates of A is ( - 2,0)

For the point B , abscissa = 0

From Equation (1) we get

$\implies \sf{2y = - 6}$

$\implies \sf{y = - 3}$

So the coordinates of B is (0,-3)

This state that the line given by Equation (1) intersects x axis at A(-2,0) and y axis at B (0,-3) respectively

FINAL ANSWER

The equation 3x + 2y + 6 = 0 intersects x axis at A(-2,0) and y axis at B (0,-3) respectively

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