The initial value of this function is the y-intercept. We know that the slope-intercept form of the equation of a line is given by:
[tex]y=mx+b \\ \\ \\ Where: \\ \\ \\ m:slope \\ \\ b:y-intercept[/tex]
Writing our equation in slope intercept form:
[tex]2x + 3y = 6 \\ \\ \\ \text{Subtract 2x from both sides}: \\ \\ 2x -2x+ 3y = 6-2x \\ \\ 3y=6-2x \\ \\ \\ \text{Divide both sides by 3}: \\ \\ y=\frac{6-2x}{3} \\ \\ y=-\frac{2x}{3}+2[/tex]
So the initial value is:
[tex]b=3[/tex]
