Question

Give the equation of four lines passing through ( −2 ,3 ).How many more such lines are there, and
why ?

Answer 1

nfinite lines can be drawn from one point .because one point no give fixed slope e.g possibility of slope is infinity hence lines can be drawn infinity.

let m is the slope of lines then ,

(y+3)=m (x-2)

y+3=mx-2m

mx-y=3+2m

hence this is family of equation which passes through (2,-3)

now ,

put m=1

x-y=5

m=2

2x-y=7

now equations x-y=5 and 2x-y=7 are two lines which passes through (2,-3)

Answer 2

☆ Given Question :-

• Give the equation of four lines pas ses thro ugh ( −2 ,3 ). How many such lines are there, and why ?

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$\huge \orange{AηsωeR}$

$\bf \:Since, \: the \: point \: is (-2, 3)$

$\bf \:∴x \: - coordinate = - \: 2$

and

$\bf \:∴y - coordinate = 3$

$\bf \:So, \: {1}^{st} \: equation \: is x + y = - 2 + 3 = 1$

$\bf\implies \:x + y = 1$

$\bf \:So, \: {2}^{nd} \: equation\: is x + 2y = - 2 + 6 = 4$

$\bf\implies \:x + 2y = 4$

$\bf \:So, \: {3}^{rd} \: equation \: is x - y = - 2 - 3 = - 5$

$\bf\implies \: - x - y = - 5$

$\bf \:So, \: {4}^{th} \: equation \: is 2x + y = - 4 + 3 = - 1$

$\bf\implies \:2x + y = - 1$

☆ So, infinitely many lines are there because across one point, infinite lines can pas ses.

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