Give the equation of the line passing through the point  
(
−
9
,
−
37
)
  that is parallel to  
y
=
4
x
+
5
 .

Write your answer in Slope-Intercept Form.

To find the equation of a line that is parallel to the line \( y = 4x + 5 \) and passes through the point \((-9, -37)\), follow these steps:

### 1. Identify the Slope of the Given Line:
The equation given is in slope-intercept form \( y = mx + b \), where \( m \) is the slope. For the line \( y = 4x + 5 \), the slope \( m \) is 4.

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

Substitute \( m = 4 \), \( x_1 = -9 \), and \( y_1 = -37 \) into the point-slope form:
\[
y - (-37) = 4(x - (-9))
\]
\[
y + 37 = 4(x + 9)
\]

### 3. Simplify to Slope-Intercept Form:
Now, simplify the equation to get it in slope-intercept form \( y = mx + b \):
\[
y + 37 = 4x + 36
\]
\[
y = 4x + 36 - 37
\]
\[
y = 4x - 1
\]

### Final Answer:
The equation of the line in slope-intercept form is:
\[
\boxed{y = 4x - 1}
\]

Would you like more details on any of these steps?

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Here are some related questions you might find interesting:
1. How do you find the equation of a line given two points?
2. What does it mean for two lines to be parallel?
3. How do you convert from point-slope form to standard form?
4. How do you find the equation of a line perpendicular to a given line?
5. What is the relationship between the slopes of parallel lines?

**Tip:** When two lines are parallel, their slopes are equal. This is key to solving many problems involving parallel lines.

Learn how to find the equation of a line that is parallel to y = 4x + 5 and passes through the point (-9, -37). This problem involves using the point-slope form and slope-intercept form of a line's equation. Suitable for students in Grades 7-9.

Math Problem Statement

Give the equation of the line passing through the point
( − 9 , − 37 ) that is parallel to
y

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