At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Discover solutions to your questions from experienced professionals across multiple fields on our comprehensive Q&A platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
To determine the equation of a line parallel to a given line, we should start by understanding that parallel lines have the same slope. Suppose the given line has the equation [tex]\( y = mx + c \)[/tex].
Given information:
1. The parallel line must have the same slope [tex]\( m \)[/tex]. Let's denote the slope as [tex]\( m = 2 \)[/tex].
2. The parallel line has an [tex]\(x\)[/tex]-intercept of 4, which means the line passes through the point (4, 0).
We need to find the [tex]\( y \)[/tex]-intercept, [tex]\( b \)[/tex], of the new line that has this [tex]\( x \)[/tex]-intercept and the same slope as the given line.
Step-by-step solution:
1. Start with the slope-intercept form of the line: [tex]\( y = mx + b \)[/tex].
2. Use the slope [tex]\( m = 2 \)[/tex] (which is the same as the slope of the original line) in the equation:
[tex]\[ y = 2x + b \][/tex]
3. Since the line passes through the point (4, 0) (given as the [tex]\( x \)[/tex]-intercept):
[tex]\[ 0 = 2(4) + b \][/tex]
4. Solve for [tex]\( b \)[/tex]:
[tex]\[ 0 = 8 + b \][/tex]
[tex]\[ b = -8 \][/tex]
So, the equation of the line parallel to the given line and with an [tex]\( x \)[/tex]-intercept of 4 is:
[tex]\[ y = 2x - 8 \][/tex]
Given information:
1. The parallel line must have the same slope [tex]\( m \)[/tex]. Let's denote the slope as [tex]\( m = 2 \)[/tex].
2. The parallel line has an [tex]\(x\)[/tex]-intercept of 4, which means the line passes through the point (4, 0).
We need to find the [tex]\( y \)[/tex]-intercept, [tex]\( b \)[/tex], of the new line that has this [tex]\( x \)[/tex]-intercept and the same slope as the given line.
Step-by-step solution:
1. Start with the slope-intercept form of the line: [tex]\( y = mx + b \)[/tex].
2. Use the slope [tex]\( m = 2 \)[/tex] (which is the same as the slope of the original line) in the equation:
[tex]\[ y = 2x + b \][/tex]
3. Since the line passes through the point (4, 0) (given as the [tex]\( x \)[/tex]-intercept):
[tex]\[ 0 = 2(4) + b \][/tex]
4. Solve for [tex]\( b \)[/tex]:
[tex]\[ 0 = 8 + b \][/tex]
[tex]\[ b = -8 \][/tex]
So, the equation of the line parallel to the given line and with an [tex]\( x \)[/tex]-intercept of 4 is:
[tex]\[ y = 2x - 8 \][/tex]
We appreciate your time. Please come back anytime for the latest information and answers to your questions. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.