https://file.aiquickdraw.com/mathbot/file/1724283175456taq2eowu.jpg

To solve this problem, we need to find the equation of a line that is parallel to the line \( y = 4x + 9 \) and passes through the point \( (2, 1) \).

### Step 1: Identify the slope of the given line
The slope-intercept form of a line is given by:
\[
y = mx + c
\]
where \( m \) is the slope and \( c \) is the y-intercept.

For the line \( y = 4x + 9 \), the slope \( m \) is 4.

### Step 2: Use the point-slope form of the line equation
The point-slope form of a line's equation is:
\[
y - y_1 = m(x - x_1)
\]
where \( (x_1, y_1) \) is a point on the line and \( m \) is the slope.

Substituting the point \( (2, 1) \) and the slope \( m = 4 \):
\[
y - 1 = 4(x - 2)
\]

### Step 3: Simplify the equation
Expand and simplify the equation:
\[
y - 1 = 4x - 8
\]
\[
y = 4x - 7
\]

### Step 4: Identify the correct answer
The equation of the line is \( y = 4x - 7 \), which corresponds to option **A**.

### Final Answer:
The correct answer is **A**: \( y = 4x - 7 \).

Would you like to go over any details or have further questions?

Here are some related questions for practice:
1. How do you find the equation of a line that is perpendicular to \( y = 4x + 9 \) and passes through \( (2, 1) \)?
2. What is the slope of a line parallel to \( y = -3x + 5 \)?
3. How do you determine if two lines are parallel or perpendicular given their equations?
4. What is the general form of a linear equation?
5. How can you find the y-intercept of a line given its equation?

**Tip:** Remember that parallel lines always have the same slope, but different y-intercepts.

Learn how to find the equation of a line parallel to y = 4x + 9 and passing through the point (2, 1) with a detailed step-by-step solution. This problem covers linear equations, slope determination, and the point-slope form of a line equation. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation