For this case, the first thing to do is find the slope of the line shown.
We have then:
[tex]m = \frac{y2-y1}{x2-x1} [/tex]
Substituting values we have:
[tex]m = \frac{7-6}{3-0} [/tex]
Rewriting:
[tex]m = \frac{1}{3} [/tex]
As the lines are parallel, then the slopes are the same.
The generic equation of the line that is looked for is:
[tex]y-yo = m (x-xo)
[/tex]
Where,
m: slope of the line
(xo, yo): point through which the line passes
Substituting values we have:
[tex]y- \frac{19}{3} = \frac{1}{3}(x-7) [/tex]
Rewriting:
[tex]y=\frac{1}{3}x - \frac{7}{3} + \frac{19}{3}[/tex]
[tex]y=\frac{1}{3}x + \frac{12}{3}[/tex]
[tex]y=\frac{1}{3}x +4[/tex]
Answer:
[tex]y=\frac{1}{3}x +4[/tex]
option C
