Given:
The equation of the line is :
[tex]3x-2y=12[/tex]
The x- intercepts are the points where the y-coordinate is zero.
Hence,
[tex]\begin{gathered} 3x-2y=12 \\ 3x-2(0)=12 \\ 3x=12 \\ x=4 \end{gathered}[/tex]
Thus, the x- intercept is (4,0)
The y-intercept is the point where x-coordinate is zero,hence
[tex]\begin{gathered} 3x-2y=12 \\ 3(0))-2y=12 \\ -2y=12 \\ y=-6 \end{gathered}[/tex]
Hence, the y-intercept is (0,- 6)
Now, the slope is given by 'm' in the standard equation of line: y = mx + c
Comparing given equation with this standard form,
[tex]\begin{gathered} 3x-2y=12 \\ -2y=-3x+12 \\ y=\frac{3}{2}x+\frac{12}{-2} \\ y=\frac{3}{2}x-6 \end{gathered}[/tex]
Hence, the slope is 3/2.
To graph the equation,plot the points (4,0) and (0,- 6 )
This is the graph of the line.
