Explanation
[tex]\begin{gathered} 1.5x+3y=9 \\ \end{gathered}[/tex]
we have the equation of a line, the best way to graph this is:
Step 1
get the slope -intercept form: to do that, isolate y
[tex]\begin{gathered} 1.5x+3y=9 \\ \text{subtract 1.5x in both sides} \\ 1.5x+3y-1.5x=9-1.5x \\ 3y=9-1.5x \\ \text{divide both sides by 3} \\ \frac{3y}{3}=\frac{9}{3}-\frac{1.5x}{3} \\ y=3-\frac{1}{2}x \\ y=-\frac{1}{2}x+3 \end{gathered}[/tex]
Step 2
now, to graph we need 2 coordinates from the line:
you can choice any input value, for example.
a) when x= 0
[tex]\begin{gathered} y=-\frac{1}{2}x+3 \\ y=-\frac{1}{2}(0)+3 \\ y=0+3 \\ y=3 \\ \text{hence, the coordinate is} \\ (0,3) \end{gathered}[/tex]
b) when x= 4
[tex]\begin{gathered} y=-\frac{1}{2}x+3 \\ y=-\frac{1}{2}(4)+3 \\ y=-2+3 \\ y=1 \\ so,\text{ the coordinate is (4,1)} \end{gathered}[/tex]
Finally, draw a lines that passes through the points (0,3) and (4,1)
I hope this helps you
