Question

Equation of a straight line
passing through (1, 2) and (2,5)
is​

Answer 1

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➠ Equation of a straight line  passing through (1, 2) and (2,5)  is​ ?

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❏ A straight line a a open 2-D figure that is made up of infinitely many points or infinitely many points lies on one straight line.

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❏ Slope of a line is the inclination of that line with coordinate x-axis.

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$\star \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \boxed { \bold {:\leadsto Slope = \dfrac{\triangle y}{\triangle x} =\dfrac{y_2 - y_1}{x_2 - x_1} } }$

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❏ If 2 co-ordinates of points are given then we can write a unique equation of line that passes through that points.

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$\star \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \boxed { \bold {:\leadsto y - y_1 =\dfrac{y_2 - y_1}{x_2 - x_1}\big[x-x_1 \big] } }$

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$\underline{\boxed{\bold{ \bigstar \; Given \; \bigstar }}}$  

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➠ Point 1 : (1,2)

➠ Point 2 : (2,5)

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Let's Start !

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❖ First of all let's have a clear look on following values.

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$\boxed { :\longmapsto x_1 = 1 \ ,\ y_1 = 2 }\\\boxed {:\longmapsto x_2= 2\ ,\ y_2 = 5 }$

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❖ Now Let's substitute the given values in our equation .-.

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$\star \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \boxed { \bold {:\leadsto y - y_1 =\dfrac{y_2 - y_1}{x_2 - x_1}\big[x-x_1 \big] } }$

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$:\implies y - 2 =\dfrac{5-2}{2 - 1}\big[x-1 \big]$

$:\implies y - 2 =\dfrac{3}{1}\big(x-1 \big)$

$:\implies y - 2 = 3(x-1)$

$:\implies y - 2 = 3x-3$

$:\implies y = 3x-3 + 2$

$\boxed { \bold { \orange {:\implies y = 3x-1 } } }$

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$\boxed{\boxed{\bold{\therefore Equation \; of \; line : y = 3x - 1}}}$

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Hope this helps u .../

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