What is an equation of the line that passes through the point left parenthesis, minus, 1, comma, minus, 5, right parenthesis(−1,−5) and is parallel to the line 6, x, minus, y, equals, 96*x*−*y*=9?


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!

What is an equation of the line that passes through the point (−1,−5) and is parallel to the line 6x−y=9?

Learn how to find the equation of a line that passes through the point (-1, -5) and is parallel to the line 6x - y = 9. This solution explains key algebraic concepts such as slope-intercept form and the parallel line theorem, ideal for Grades 9-11.

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