Answer:
[tex]y=-\frac{2}{3} x-2[/tex]
Step-by-step explanation:
the general equation for a line is:
[tex]y=mx+b[/tex]
where [tex]m[/tex] is the slope of the line, and [tex]b[/tex] is the y-intercept.
Since we need a slope of -2/3:
[tex]m=-\frac{2}{3}[/tex],
So far we have that the line must have the equation:
[tex]y=-\frac{2}{3} x+b[/tex]
the graph of a line with a negative slope is one that "falls" from left to right in the plane. And the number [tex]\frac{2}{3}[/tex] means that it falls at a ratio of 2 units in the y-axis for every 3 in the x-axis.
we are told that the y-intercept is that of the line:
[tex]y=\frac{2}{3} x-2[/tex] --> here the y-intercept is -2.
Thus the equation of the line we are looking for is:
[tex]y=-\frac{2}{3} x-2[/tex]
which means that this line crosses the y-axis at -2, and the graph is the one in the attached image.
