We will solve as follows:
First, we rewrite it in slope-intercept form:
[tex]2y-4=3x\Rightarrow2y=3x+4[/tex][tex]\Rightarrow y=\frac{3}{2}x+2[/tex]Second, to graph it we find two points using the equation and then plot the line using them. I will find the points for which x = 0 & y = 0, but any point in the line will work. That is:
*For x = 0:
[tex]y=\frac{3}{2}(0)+2\Rightarrow y=2[/tex]So, we have the point:
[tex]A(0,2)[/tex]*For y = 0:
[tex]2(0)-4=3x\Rightarrow3x=-4[/tex][tex]\Rightarrow x=-\frac{4}{3}[/tex]So, we have the point:
[tex]B(-\frac{4}{3},0)[/tex]Now, we plot the line using those points:
