Question

Identify the slope and the y - intercept of the line 3x - 2y = 12, then graph the linear linear equation.

Answer 1

The general equation in slope intercept form is given by

`\begin{gathered} y=mx+c \\ \text{where y is the slope and c is the y intercept} \end{gathered}`

The given equation is

`\begin{gathered} 3x-2y=12 \\ \text{Rewrite the equation by adding 2y to both sides} \\ 3x-2y+2y=12+2y \\ 3x=12+2y \\ \text{Subtract 12from both sides} \\ 3x-12=12-12+2y \\ 3x-12=2y \\ \text{Divide both sides by 2 } \\ (3)/(2)x-6=y \\ y=(3)/(2)x-6 \\ \text{where }(3)/(2)\text{ is the slope and -6 is the y intercept comparing it with y=mx+c} \end{gathered}`

Put y=0 to the equation to get the x intercept.

`\begin{gathered} 0=(3)/(2)x-6 \\ (3)/(2)x=6 \\ x=(6\ast2)/(3)=4 \end{gathered}`

Now plot the graph by joining coordinates of y intercept (0,-6) and coordinates of x intercept (4,0)