The problem from your screenshot asks you to write an equation in slope-intercept form for a line that passes through the given point $(-9, -3)$ and is parallel to the line given by the equation $y = -3x + 5$.

Solution:

1. Slope of the Parallel Line: The equation of the given line is $y = -3x + 5$. This is already in slope-intercept form $y = mx + b$, where $m$ is the slope.

   Since the given line has a slope of $m = -3$, the line parallel to it will have the same slope of $-3$.

2. Point-Slope Form Equation: To find the equation of the line passing through the point $(-9, -3)$ and having a slope of $-3$, we use the point-slope form:

   $y - y_1 = m(x - x_1)$ Here, $m = -3$, $x_1 = -9$, and $y_1 = -3$.

   Substituting the values: $y - (-3) = -3(x - (-9))$ Simplifying: $y + 3 = -3(x + 9)$

   Distribute the $-3$: $y + 3 = -3x - 27$

   Subtract 3 from both sides to isolate $y$: $y = -3x - 30$

Thus, the equation of the line in slope-intercept form is:

$y = -3x - 30$

Would you like further explanation on any of the steps, or do you have any questions?

5 Related Questions:

1. How do you find the slope of a line from two points?
2. What is the difference between point-slope form and slope-intercept form?
3. How do you determine if two lines are parallel based on their equations?
4. How would you find the equation of a line perpendicular to a given line?
5. How do you convert between different forms of linear equations?

Tip: For parallel lines, always remember they share the same slope!