Question

if the slope of the line passing through the point (2,5) and (-4,k) is 3/2, then the value of k is​

Answer 1

Given :

• Slope of the line passing through the point (2,5) and (-4,k) is 3/2 .

To Find :

• Value of k .

Solution :

$\longmapsto\tt{{x}_{1}=2}$

$\longmapsto\tt{{x}_{2}=-4}$

$\longmapsto\tt{{y}_{1}=5}$

$\longmapsto\tt{{y}_{2}=k}$

Using Formula :

$\longmapsto\tt\boxed{m=\dfrac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}}$

Putting Values :

$\longmapsto\tt{\dfrac{3}{2}=\dfrac{k-5}{-4-2}}$

$\longmapsto\tt{\dfrac{3}{2}=\dfrac{k-5}{-6}}$

Cross Multiply :

$\longmapsto\tt{-6(3)=2(k-5)}$

$\longmapsto\tt{-18=2k-10}$

$\longmapsto\tt{-18+10=2k}$

$\longmapsto\tt{-8=2k}$

$\longmapsto\tt{k=\cancel\dfrac{-8}{2}}$

$\longmapsto\tt\bf{k=-4}$

So , The Value of k is -4 .

Answer 2

Question :

• If the slope of the line passing through the point (2,5) and (-4,k) is 3/2, then the value of k is?

Answer :

• The value of k is -4

Step by step explanation :

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Using formula :

$\qquad\red\bigstar\:{\underline{\boxed{\bf{\green{m = \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}}}}}}}$

Putting all known values :

$\rightarrow\qquad\sf \dfrac{3}{2} = \dfrac{k - 5}{-4 - 2}$

$\rightarrow\qquad\sf \dfrac{3}{2} = \dfrac{k - 5}{-6}$

By cross multiplication :

$\rightarrow\qquad\sf 3 \:\times\: -6 = 2(k - 5)$

$\rightarrow\qquad\sf -18 = 2k - 10$

$\rightarrow\qquad\sf -18 + 10 = 2k$

$\rightarrow\qquad\sf -8 = 2k$

$\rightarrow\qquad\sf \dfrac{-8}{2} = k$

$\rightarrow\qquad\sf \dfrac{\cancel{-8}}{\cancel{2}} = k$

$\rightarrow\qquad{\boxed{\frak{k = \pink{-4}}}}\:\purple\bigstar$

$\therefore\:{\underline{\sf{Hence,\:the\:value\:of\:k\:is\:\bf{-4}\:\sf{respectively}.}}}$

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More to know :

• For finding distance between two points, we use distance formula ,i.e,$\sf \sqrt{\bigg(x_{2} - x_{1}\bigg)^2 + \bigg(y_{2} - y_{1}\bigg)^2}$
• For finding the ratio in which a line segment is divided by a point, we use section formula ,i.e, $\sf \bigg(\dfrac{m_{1}x_{2} + m_{2}x_{1}}{m_{1} + m_{2}}\:,\:\dfrac{m_{1}y_{2} + m_{2}y_{1}}{m_{1} + m_{2}}\bigg)$