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
