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