Answer:
[tex]y=-\frac{2}{3}x-2[/tex]
Step-by-step explanation:
First of all, the equation of a line is written in the standard form when it is written in the form
[tex]y=mx+q[/tex]
where
m is the slope of the line
q is the y-intercept
In this problem, we see that only the last 2 equations are written in the standard form, so the correct option must be one of those two.
We can verify what is the correct expression for the line by choosing two points along the line and substituting into the 2 equations: the equation must be valid for both points.
Here we choose the two points
A(-3,0)
B(0,-2)
The 3rd equation is [tex]y=-\frac{2}{3}x-2[/tex]
Substituting (-3,0):
[tex]0=-\frac{2}{3}(-3)-2 \rightarrow 0=+2-2[/tex] (true)
Substituting (0,-2):
[tex]-2=-\frac{2}{3}(0)-2 \rightarrow -2=-2[/tex] (true)
So, this is the correct equation.
We notice that the 4th equation cannot be correct, because it has a positive slope (2/3), while from the graph we can see that the line has a negative slope.
