Identify the Line Equation with Slope 9y Passing Through (-5, -8)

To solve this problem, we'll follow these steps:

• Step 1: Identify the given information
• Step 2: Apply the point-slope formula
• Step 3: Convert to slope-intercept form and verify against the given choices

Now, let's work through each step:
Step 1: The problem states the line passes through point $(-5, -8)$ and has a slope of $9$.
Step 2: Using the point-slope form equation, $y-y_1 = m(x-x_1)$, plug in $(x_1, y_1) = (-5, -8)$ and $m = 9$. So the equation becomes:

$y - (-8) = 9(x - (-5))$

Which simplifies to:

$y + 8 = 9(x + 5)$

Simplifying further gives:

$y + 8 = 9x + 45$

Then, bring the $8$ to the right side to solve for $y$ in terms of $x$:

$y = 9x + 45 - 8$ $y = 9x + 37$

Therefore, the equation of the line in slope-intercept form is $y = 9x + 37$, which corresponds to choice $1$.

Therefore, the solution to the problem is $y = 9x + 37$.