Determine the Linear Equation: Slope -3 Through Point (-6, -3)

To determine the equation of the given linear function, follow these steps:

• Step 1: Identify the key information: the slope $m = -3$ and the point $(-6, -3)$.
• Step 2: Use the point-slope form, $y - y_1 = m(x - x_1)$.
• Step 3: Substitute the values $m = -3$, $x_1 = -6$, and $y_1 = -3$ into the formula.
• Step 4: Solve for $y$ to convert to slope-intercept form $y = mx + b$.

Now, let's go through the process:

Use the point-slope form:

$y - (-3) = -3(x - (-6))$

Simplify the equation:

$y + 3 = -3(x + 6)$

Distribute the slope on the right side:

$y + 3 = -3x - 18$

Subtract 3 from both sides to solve for $y$:

$y = -3x - 18 - 3$

which simplifies to:

$y = -3x - 21$

This equation, $y = -3x - 21$, matches the first choice in the provided options.

Therefore, the equation that represents the function is $y = -3x - 21$.