Equation of a line in slope-intercept form
y = mx + b
where m is the slope and b is the y-intercept.
Two lines are parallel if they have the same slope. In the line:
[tex]y=-\frac{2}{3}x+\frac{5}{3}[/tex]
m = -2/3 and b = 5/3. Then, its slope is -2/3.
Substituting with m = -2/3 and the point (-3, 5), that is, x = -3 and y = 5 into the general equation, we get:
[tex]\begin{gathered} 5=(-\frac{2}{3})\cdot(-3)+b \\ 5=2+b \\ \text{ Subtracting 2 at both sides:} \\ 5-2=2+b-2 \\ 3=b \end{gathered}[/tex]
Finally, substituting with m = -2/3 and b = 3 into the general equation, the equation is:
[tex]y=-\frac{2}{3}x+3[/tex]
