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[tex]3y = 2x - 3[/tex]
Divide sides by 3
[tex] \frac{3}{3} y = \frac{2}{3} x - \frac{3}{3} \\ [/tex]
[tex]y = \frac{2}{3}x - 1 \\ [/tex]
This is the slope-intercept form of the given line.
The coefficient of x in slope-intercept form of the linear functions shows the slope .
Thus the slope of the given line is ⅔ .
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Remember from now on ;
Multiply of the slopes of the lines which are perpendicular to each other equals -1.
Suppose the slope of the line which question asked is m .
So :
[tex] \frac{2}{3} \times m = - 1 \\ [/tex]
Multiply sides by 3
[tex]3 \times \frac{2}{3} \times m = 3 \times ( - 1) \\ [/tex]
[tex]2m = - 3[/tex]
Divide sides by 2
[tex] \frac{2}{2} m = \frac{ - 3}{2} \\ [/tex]
[tex]m = - \frac{3}{2} \\ [/tex]
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[tex]y - 6 = - \frac{2}{3}(x - 0) \\ [/tex]
[tex]y = - \frac{2}{3} x + 6 \\ [/tex]
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