Answer
$y=\dfrac{2}{3}x+\dfrac{19}{3}$ or, in general form, $2x-3y+19=0$
Work Step by Step
Through $(1,7);$ slope $\frac{2}{3}$
Use the point-slope form of the equation of a line, which is $y-y_{1}=m(x-x_{1})$, where $(x_{1},y_{1})$ is a point through which the line passes and $m$ is the slope.
Both $(x_{1},y_{1})$ and $m$ are given. Substitute them into the formula and simplify to obtain the equation of this line:
$y-y_{1}=m(x-x_{1})$
$y-7=\dfrac{2}{3}(x-1)$
$y-7=\dfrac{2}{3}x-\dfrac{2}{3}$
$y=\dfrac{2}{3}x-\dfrac{2}{3}+7$
$y=\dfrac{2}{3}x+\dfrac{19}{3}$ or, in general form, $2x-3y+19=0$
