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[tex]3y - 4x = - 8[/tex]
Add sides 4x
[tex]3y - 4x + 4x = 4x - 8[/tex]
[tex]3y = 4x - 8[/tex]
Divide sides by 3
[tex] \frac{3}{3} y = \frac{4}{3} x - \frac{8}{3} \\ [/tex]
[tex]y = \frac{4}{3} x - 8 \\ [/tex]
This is the slope-intercept form of the line.
We that the coefficient of the x in slope-intercept form , is the slope of the line.
Thus ;
[tex]slope = \frac{4}{3} \\ [/tex]
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Remember from now on ;
Multiply of the slopes of the lines which are perpendicular to each other equal -1 .
Suppose the slope of the line which question asked is m.
So :
[tex] \frac{3}{4} \times m = - 1 \\ [/tex]
Multiply sides by 4
[tex]4 \times \frac{3}{4} \times m = 4 \times ( - 1) \\ [/tex]
[tex]3m = - 4[/tex]
Divide sides by 3
[tex] \frac{3}{3} m = \frac{ - 4}{3} \\ [/tex]
[tex]m = - \frac{4}{3} \\ [/tex]
Done...
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