What is an equation of the line that passes through the point left parenthesis, minus, 1, comma, 1, right parenthesis(−1,1) and is parallel to the line 3, x, plus, y, equals, 93*x*+*y*=9?

To find the equation of a line that passes through the point \((-1, 1)\) and is parallel to the line \(3x + y = 9\), follow these steps:

### Step 1: Determine the slope of the given line
The given line is in the form \(3x + y = 9\). To find its slope, rewrite this in slope-intercept form \(y = mx + b\), where \(m\) is the slope:

\[
y = -3x + 9
\]

Here, the slope \(m = -3\).

### Step 2: Use the slope-point form of the equation of a line
Since the lines are parallel, the slope of the required line is also \(m = -3\). Now, use the slope-point form of the equation of a line:

\[
y - y_1 = m(x - x_1)
\]

where \((x_1, y_1)\) is the point \((-1, 1)\) and \(m = -3\). Substituting these values:

\[
y - 1 = -3(x + 1)
\]

### Step 3: Simplify the equation
Now, expand and simplify the equation:

\[
y - 1 = -3x - 3
\]

Add 1 to both sides:

\[
y = -3x - 2
\]

### Final Equation
The equation of the line that passes through the point \((-1, 1)\) and is parallel to the line \(3x + y = 9\) is:

\[
y = -3x - 2
\]

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Would you like more details or have any questions?

Here are 5 related questions:
1. How do you find the equation of a line given two points?
2. How would you find the slope if the equation was given in another form?
3. What is the difference between parallel and perpendicular lines in terms of slopes?
4. How would the equation change if the line was perpendicular instead of parallel?
5. How can you convert a line equation to different forms like point-slope or standard form?

**Tip:** When lines are parallel, they always have the same slope.

What is an equation of the line that passes through the point (-1,1) and is parallel to the line 3x + y = 9?

Learn how to find the equation of a line that passes through the point (-1, 1) and is parallel to the line 3x + y = 9. This step-by-step solution covers key algebraic concepts like slope-intercept form and point-slope form. Ideal for students in Grades 8-10.

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