For what value of k does kx + 7y = 10 have a slope of 3?

Answers

Answer 1

Answer:

k = -21

Step-by-step explanation:

Slope y-intercept form : y = mx +c

kx + 7y = 10

        7y = -kx + 10

          y = [tex]\frac{-k}{7}x+\frac{10}{7}[/tex]

[tex]\frac{-k}{7}=3\\\\ -k = 3*7\\\\ -k = 21\\\\ k = -21[/tex]

Answer 2

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Hint :

[tex]slope = The \: \: coefficient \: \: of \: \: x \: \: in \: \: the \: \: slope-intercept \: \: form \\ [/tex]

_________________________________

Thus we need to find the slope-intercept form of the line which must be like this :

[tex]y = ax + b[/tex]

Let's do it...

[tex]7y + kx = 10[/tex]

Subtract sides kx

[tex]7y + kx - kx = 10 - kx[/tex]

[tex]7y = 10 - kx[/tex]

[tex] 7y = - kx + 10[/tex]

Divide sides by 7

[tex] \frac{7y}{7} = \frac{ - kx + 10}{7} \\ [/tex]

[tex]y = \frac{ - kx}{7} + \frac{10}{7} \\ [/tex]

[tex]y = - \frac{k}{7} x + \frac{10}{7} \\ [/tex]

This is the slope-intercept form .

[tex]The \: \: coefficient \: \: of \: \: x = - \frac{k}{7} \\ [/tex]

The slope is 3 ,

Thus :

[tex] - \frac{k}{7} = 3 \\ [/tex]

Multiply sides by 7

[tex]7 \times ( - \frac{k}{7}) = 7 \times 3 \\ [/tex]

[tex] - k = 21[/tex]

Multiply sides by - 1

[tex] ( - 1) \times ( - k) = ( - 1) \times (21)[/tex]

[tex]k = - 21[/tex]

And we're done....

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Step-by-step explanation:

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------------------------

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Answers

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Answers

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Answers

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Answers

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