Answer: The correct option is
(C) [tex]y=\dfrac{2}{3}x-2.[/tex]
Step-by-step explanation: We are given to select the equation of a line in slope-intercept form with slope [tex]\dfrac{2}{3}[/tex] and y-intercept at (0, -2).
We know that
the slope-intercept form of the equation of a line with slope m and y -intercept at the point (0, c) is given by
[tex]y=mx+c.[/tex]
For the given line, we have
[tex]\textup{slope, }m=\dfrac{2}{3},\\\\\\\textup{y-intercept},~(0,c)=(0,-2)\\\\\Rightarrow c=-2.[/tex]
Therefore, the equation of the line in slope-intercept form is
[tex]y=mx+c\\\\\Rightarrow y=\dfrac{2}{3}x+(-2)\\\\\\\Rightarrow y=\dfrac{2}{3}x-2.[/tex]
Thus, the required equation of the line in slope-intercept form is [tex]y=\dfrac{2}{3}x-2.[/tex]
Option (C) is CORRECT.
