To find the equation of a line that passes through the point $(-1, -5)$ and is parallel to the line $6x - y = 9$, we need to follow these steps:

Step 1: Find the slope of the given line

The equation of the given line is $6x - y = 9$. We will rewrite this in slope-intercept form $y = mx + b$, where $m$ is the slope.

Start by solving for $y$: 6x - y = 9 \quad \text{(subtract 6x from both sides)} -y = -6x + 9 \quad \text{(multiply through by -1$to solve for$y)} $y = 6x - 9$ So, the slope of the given line is $m = 6$.

Step 2: Use the slope-point form of the line equation

Since the line we are looking for is parallel to the given line, it has the same slope $m = 6$. Now, we use the point-slope form of the equation of a line: $y - y_1 = m(x - x_1)$ where $(x_1, y_1)$ is the point $(-1, -5)$ and $m = 6$.

Substitute the values: $y - (-5) = 6(x - (-1))$ $y + 5 = 6(x + 1)$ $y + 5 = 6x + 6$ Now, solve for $y$: $y = 6x + 6 - 5$ $y = 6x + 1$

Final Answer:

The equation of the line is: $y = 6x + 1$

Would you like more details or have any questions?

Related Questions:

1. How do you find the slope of a line from its equation?
2. What is the significance of parallel lines in terms of slopes?
3. How do you convert a line equation into slope-intercept form?
4. How would the equation change if the lines were perpendicular instead of parallel?
5. Can you explain how to derive the point-slope form of a line equation?

Tip:

When two lines are parallel, their slopes are always equal. Use this fact to quickly determine the slope of a parallel line from a given equation!