Question

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

Answer 1

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Hint :

`slope = The \: \: coefficient \: \: of \: \: x \: \: in \: \: the \: \: slope-intercept \: \: form \\`

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

`y = ax + b`

Let's do it...

`7y + kx = 10`

Subtract sides kx

`7y + kx - kx = 10 - kx`

`7y = 10 - kx`

`7y = - kx + 10`

Divide sides by 7

`(7y)/(7) = ( - kx + 10)/(7) \\`

`y = ( - kx)/(7) + (10)/(7) \\`

`y = - (k)/(7) x + (10)/(7) \\`

This is the slope-intercept form .

`The \: \: coefficient \: \: of \: \: x = - (k)/(7) \\`

The slope is 3 ,

Thus :

`- (k)/(7) = 3 \\`

Multiply sides by 7

`7 * ( - (k)/(7)) = 7 * 3 \\`

`- k = 21`

Multiply sides by - 1

`( - 1) * ( - k) = ( - 1) * (21)`

`k = - 21`

And we're done....

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Answer 2

k = -21

Explanation:

Slope y-intercept form : y = mx +c

kx + 7y = 10

7y = -kx + 10

y =
`(-k)/(7)x+(10)/(7)`

`(-k)/(7)=3\\\\ -k = 3*7\\\\ -k = 21\\\\ k = -21`