Question
Write an equation for line L in point-slope form and slope-intercept form.
L is parallel to y equals 4 x.
-6
-4
-2
2
4
6
-6
-4
-2
2
4
6
x
y
y equals 4 xleft parenthesis 2 comma negative 1 right parenthesisUpper L
A coordinate system has a horizontal x-axis labeled from negative 6 to 6 in increments of 1 and a vertical y-axis labeled from negative 6 to 6 in increments of 1. From left to right, a line rises in quadrant 3 and passes through the origin into quadrant 1 and is labeled y = 4 x. A second line labeled L rises from left to right parallel to the first line passing through the plotted point (2, negative 1).
.
.
.
Question content area right
Part 1
Write an equation for line L in point-slope form.
enter your response here
(Simplify your answer. Use integers or fractions for any numbers in the equation.)
L is parallel to y equals 4 x.
-6
-4
-2
2
4
6
-6
-4
-2
2
4
6
x
y
y equals 4 xleft parenthesis 2 comma negative 1 right parenthesisUpper L
A coordinate system has a horizontal x-axis labeled from negative 6 to 6 in increments of 1 and a vertical y-axis labeled from negative 6 to 6 in increments of 1. From left to right, a line rises in quadrant 3 and passes through the origin into quadrant 1 and is labeled y = 4 x. A second line labeled L rises from left to right parallel to the first line passing through the plotted point (2, negative 1).
.
.
.
Question content area right
Part 1
Write an equation for line L in point-slope form.
enter your response here
(Simplify your answer. Use integers or fractions for any numbers in the equation.)
Answers
GPT-4o mini
To write the equation of line \( L \) in point-slope form and slope-intercept form, we first need to determine the characteristics of line \( L \).
### Given:
- Line \( L \) is parallel to the line \( y = 4x \).
- The slope of the line \( y = 4x \) is \( 4 \).
- Line \( L \) passes through the point \( (2, -1) \).
### Part 1: Point-Slope Form
The point-slope form of the equation of a line is given by:
\[
y - y_1 = m(x - x_1)
\]
where \( m \) is the slope, and \( (x_1, y_1) \) is a point on the line.
Substituting \( m = 4 \) and \( (x_1, y_1) = (2, -1) \):
\[
y - (-1) = 4(x - 2)
\]
This simplifies to:
\[
y + 1 = 4(x - 2)
\]
### Final Answer in Point-Slope Form:
\[
y + 1 = 4(x - 2)
\]
---
### Part 2: Slope-Intercept Form
To convert the point-slope form to slope-intercept form \( y = mx + b \), we start from the point-slope form we derived:
\[
y + 1 = 4(x - 2)
\]
Distributing \( 4 \) on the right side:
\[
y + 1 = 4x - 8
\]
Now, subtract \( 1 \) from both sides:
\[
y = 4x - 9
\]
### Final Answer in Slope-Intercept Form:
\[
y = 4x - 9
\]
### Summary:
- Point-Slope Form: \( y + 1 = 4(x - 2) \)
- Slope-Intercept Form: \( y = 4x - 9 \)
### Given:
- Line \( L \) is parallel to the line \( y = 4x \).
- The slope of the line \( y = 4x \) is \( 4 \).
- Line \( L \) passes through the point \( (2, -1) \).
### Part 1: Point-Slope Form
The point-slope form of the equation of a line is given by:
\[
y - y_1 = m(x - x_1)
\]
where \( m \) is the slope, and \( (x_1, y_1) \) is a point on the line.
Substituting \( m = 4 \) and \( (x_1, y_1) = (2, -1) \):
\[
y - (-1) = 4(x - 2)
\]
This simplifies to:
\[
y + 1 = 4(x - 2)
\]
### Final Answer in Point-Slope Form:
\[
y + 1 = 4(x - 2)
\]
---
### Part 2: Slope-Intercept Form
To convert the point-slope form to slope-intercept form \( y = mx + b \), we start from the point-slope form we derived:
\[
y + 1 = 4(x - 2)
\]
Distributing \( 4 \) on the right side:
\[
y + 1 = 4x - 8
\]
Now, subtract \( 1 \) from both sides:
\[
y = 4x - 9
\]
### Final Answer in Slope-Intercept Form:
\[
y = 4x - 9
\]
### Summary:
- Point-Slope Form: \( y + 1 = 4(x - 2) \)
- Slope-Intercept Form: \( y = 4x - 9 \)