Explanation
Step 1
get the slope-intercep form_
we need to use the function to graph the line,so let's convert the given equation in the slope-intercept form,to do that, isolate y
so
[tex]\begin{gathered} -6x+9y=0 \\ \text{add 6x in both sides } \\ -6x+9y+6x=0+6x \\ 9y=6x \\ \text{divide both sides by }9 \\ \frac{9y}{9}=\frac{6x}{9} \\ y=\frac{2}{3}x \end{gathered}[/tex]
so, the equation of the line is
[tex]y=\frac{2}{3}x[/tex]
Step 2
now, let's use the equation to find 2 coordiantes of the line
a) for x =0
[tex]\begin{gathered} y=\frac{2}{3}x \\ \text{replace} \\ y=\frac{3}{2}(0)=0 \\ \text{hence, } \\ \text{ Point 1 ( 0,0)} \end{gathered}[/tex]
b) for x= 3
[tex]\begin{gathered} y=\frac{2}{3}x \\ \text{replace} \\ y=\frac{2}{3}(3)=2 \\ \text{hence, } \\ \text{ Point 1 ( 3,2)} \end{gathered}[/tex]
Step 3
finally, draw a line that passes through the points (0,0) and (3,2)
I hope this helps you
