Answer:
[tex]y=\displaystyle\frac{2}{3}x[/tex]
Step-by-step explanation:
Hi there!
The given linear equations are organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope of the line and b is the y-intercept (the value of y when x=0)
First, we can determine the slope using the following formula:
[tex]m=\displaystyle\frac{y_2-y_1}{x_2-x_1}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in any two points from the graph that falls on the line (you can see below that I've used (3,2) and (0,0):
[tex]m=\displaystyle\frac{2-0}{3-0}\\\\m=\displaystyle\frac{2}{3}[/tex]
Therefore, the slope of the line is [tex]\displaystyle\frac{2}{3}[/tex]. Plug this into [tex]y=mx+b[/tex] as m:
[tex]y=\displaystyle\frac{2}{3}x+b[/tex]
We know that the point (0,0) falls on the line. Because y=0 when x=0, we know that the y-intercept (b) is 0:
[tex]y=\displaystyle\frac{2}{3}x+0\\\\y=\displaystyle\frac{2}{3}x[/tex]
I hope this helps!
