Answer :
hello
the easiest way to solve this problem is to pick each equation and solve for the slope and intercept separately.
an edge over this is to mirror the standard linear equation and use it for reference in our questions
[tex]\begin{gathered} y=mx+c \\ m=\text{slope} \\ c=\text{intercept} \end{gathered}[/tex]the equations given are
[tex]\begin{gathered} 3x-2y=6 \\ 2x+3y=12 \\ 3y+6=2x \end{gathered}[/tex]from the first equation
[tex]3x-2y=6[/tex]step 1: make y the subject of formula
[tex]\begin{gathered} 3x-2y=6 \\ 2y=3x-6 \\ \text{divide both sides by the coefficient of y} \\ \frac{2y}{2}=\frac{3x-6}{2} \\ y=\frac{3x}{2}-\frac{6}{2} \\ y=\frac{3}{2}x-3 \end{gathered}[/tex]from this, we can see that (m = slope) here is equal to 3/2 and the intercept (y = -3)
the first equation gives us a slope of 3/2 and an intercept of y = -3
the second equation is
[tex]2x+3y=12[/tex]repeat the same process for equation 1
[tex]\begin{gathered} 2x+3y=12 \\ \text{make y the subject of formula} \\ 3y=12-2x \\ \text{divide through the sides by the coefficient of y} \\ \frac{3y}{3}=\frac{12-2x}{3} \\ y=\frac{12}{3}-\frac{2}{3}x \\ y=4-\frac{2}{3}x \\ \text{rearrange the equation to mirror y = mx + c} \\ y=-\frac{2}{3}x+4 \\ \text{slope}=-\frac{2}{3} \\ \text{ intercept=4} \end{gathered}[/tex]the slope in this equation is equal to -2/3 and the intecept equal 4
the third equation
[tex]\begin{gathered} 3y+6=2x \\ \text{make y the subject of formula} \\ 3y=2x-6 \\ \text{divide through by the coefficient of y} \\ \frac{3y}{3}=\frac{2x-6}{3} \\ y=\frac{2}{3}x-2 \\ \text{slope}=\frac{2}{3} \\ \text{ intercept=-2} \end{gathered}[/tex]from the calculation above, the slope and intercept of the equation is 2/3 and -2 respectively