#### Answer

$y=\dfrac{2}{3}x+\dfrac{19}{3}$

#### Work Step by Step

RECALL:
The slope-intercept form of a line's equation is $y=mx+b$ where m = slope and b = y-intercept.
The given line has $m=\frac{2}{3}$ and passes through the point $(1, 7)$.
Thus, the tentative equation of the line is:
$y=\dfrac{2}{3}(x)+b$
To find the value of $b$, substitute the coordinates of $(1, 7)$ into the tentative equation above to obtain:
$y=\dfrac{2}{3}x+b
\\7 = \dfrac{2}{3}(1) + b
\\7 = \dfrac{2}{3} + b
\\7-\dfrac{2}{3} = b
\\\dfrac{21}{3} - \dfrac{2}{3}=b
\\\dfrac{19}{3} = b$
Therefore, the equation of the line is:
$y=\dfrac{2}{3}x+\dfrac{19}{3}$