Answer
The $y$-value of the $y$-intercept is $\frac{15}{7}$.
Work Step by Step
We want to convert this equation to the slope-intercept form so that we can easily locate the slope of this line. The slope-intercept form is given by the formula:
$y = mx + b$
where $m$ is the slope and $b$ is the $y$-value of the $y$-intercept.
Let's solve this equation for $y$.
Subtract $5x$ from both sides of the equation to isolate the $y$ term on the left side:
$-7y = -5x - 15$
Divide both sides of the equation by $-7$ to solve for $y$:
$y = \dfrac{5}{7}x + \dfrac{15}{7}$
The $y$-value of the $y$-intercept is $\frac{15}{7}$.
