Question
rough: \( (-2,1) \), parallel to \( y=3 x-1 \)
Ask by Reese Ortega. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The equation of the line parallel to \( y = 3x - 1 \) that passes through the point \( (-2, 1) \) is \( y = 3x + 7 \).
Solution
To find the equation of a line that is **parallel** to \( y = 3x - 1 \) and **passes through the point** \( (-2, 1) \), follow these steps:
1. **Determine the slope of the given line:**
The equation \( y = 3x - 1 \) is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope.
So, the slope \( m \) of the given line is **3**.
2. **Use the slope-point form for the new line:**
Since parallel lines have the **same slope**, the new line will also have a slope of **3**.
The point-slope form of a line is:
\[
y - y_1 = m(x - x_1)
\]
where \( (x_1, y_1) \) is a point on the line, and \( m \) is the slope.
Plugging in the slope and the given point \( (-2, 1) \):
\[
y - 1 = 3(x - (-2)) \\
y - 1 = 3(x + 2)
\]
3. **Simplify the equation to slope-intercept form:**
Distribute the slope on the right side:
\[
y - 1 = 3x + 6
\]
Add **1** to both sides to solve for \( y \):
\[
y = 3x + 7
\]
**Final Equation:**
\[
y = 3x + 7
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To find the equation of a line that is parallel to \( y=3x-1 \) and passes through the point \( (-2,1) \), start with the slope. The slope of the given line is 3, so the new line will also have a slope of 3. Using the point-slope form of a line: \[ y - y_1 = m(x - x_1) \] Plugging in \( m = 3 \), \( x_1 = -2 \), and \( y_1 = 1 \): \[ y - 1 = 3(x + 2) \] Expanding and simplifying: \[ y - 1 = 3x + 6 \] \[ y = 3x + 7 \] So, the equation of the line is \( y = 3x + 7 \).
