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Sagot :
We want to determine the slope of the equation;
[tex]\frac{1}{2}x+\frac{1}{3}y=1[/tex]We need to express the equation in the slope-intercept form;
[tex]y=mx+c[/tex]where m is the slope and c is the intercept.
Firstly, let's multiply the equation through by 3;
[tex]\begin{gathered} \frac{1\times3}{2}x+\frac{1\times3}{3}y=1\times3 \\ \frac{3}{2}x+y=3 \end{gathered}[/tex]Then, let's subtract (3/2)x from both sides;
[tex]\begin{gathered} \frac{3}{2}x-\frac{3}{2}x+y=3-\frac{3}{2}x \\ y=-\frac{3}{2}x+3 \end{gathered}[/tex]comparing the resulting equation to the slope-intercept form of straight line equation, then the slope is the coefficient of x;
[tex]slope(m)=-\frac{3}{2}[/tex]The slope of the line is -3/2
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