Answer :
Step-by-step explanation:
Given equation of line is:
[tex] 3x + y = 3\\\\
\therefore y = - 3x + 3\\\\[/tex]
Equating it with [tex] y = m_1x+c[/tex] we find:
[tex] m_1=-3[/tex]
Let the slope of required line be [tex] m_2[/tex]
[tex] \because [/tex] Required line is parallel to the given line.
[tex] \therefore\: m_2=\frac{-1}{m_1}=\frac{-1}{-3}=\frac{1}{3}[/tex]
[tex] \because [/tex] Required line passes through (2, 2) and has a slope [tex] m_2=\frac{1}{3}[/tex]
[tex] \therefore[/tex] Equation of line in slope point form is given as:
[tex] y - y_1 = m_2(x-x_1) \\\\
\therefore y- 2=\frac{1}{3}(x-2)\\\\
\therefore y- 2=\frac{1}{3}x-\frac{2}{3}\\\\
\therefore y=\frac{1}{3}x+2-\frac{2}{3}\\\\
\therefore y=\frac{1}{3}x+\frac{2\times 3-2}{3}\\\\
\therefore y=\frac{1}{3}x+\frac{4}{3}\\\\[/tex]
Equating it with [tex] y = mx+c[/tex] we find:
y-intercept [tex] (c) =\frac{4}{3}[/tex]