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a line with a slope of 2 passes through (k,3) and (6,k) on the coordinate grid. what is the value of k?

Respuesta :

Answer:

k = 5

Step-by-step explanation:

Calculate the slope m and then equate to 2

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (k, 3) and (x₂, y₂ ) = (6, k)

m = [tex]\frac{k-3}{6-k}[/tex] = 2 ( cross- multiply )

2(6 - k) = k - 3

12 - 2k = k - 3 ( subtract k from both sides )

12 - 3k = - 3 ( subtract 12 from both sides )

- 3k = - 15 ( divide both sides by - 3 )

k = 5

deepakrai138

The value of k will be 5.

Given,

A line passes through (k,3) and (6,k) on the coordinate grid.

Slope of line is 2.

We know that, slope of line passing through two point will be,

[tex]\rm m=\dfrac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]

On putting the values of all the points we get,

[tex]\rm m=\dfrac{k-3}{6-k}[/tex]

Since the slope of line is 2 as given in question, we get

[tex]\rm 2=\dfrac{k-3}{6-k}[/tex]

[tex]2(6-k)=k-3[/tex]

[tex]12-2k=k-3\\3k=15\\k=5[/tex]

Hence the value of k is 5.

For more details on slope of line follow the link:

https://brainly.com/question/2514839

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