Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Our platform provides a seamless experience for finding reliable answers from a knowledgeable network of professionals. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
To determine the equation of a line parallel to a given line that has an \( x \)-intercept of 4, we need to follow these steps:
1. Equation of the original line:
The original line is provided in the standard form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
2. Parallel line characteristics:
Parallel lines have the same slope (\( m \)). Therefore, the new line will have the same slope as the original line.
3. Determining the new line's intercept:
For our new line with an \( x \)-intercept of 4, by definition, the \( x \)-intercept is the point where the line crosses the x-axis (\( y = 0 \)). Hence, if we substitute \( x = 4 \) into the line's equation, we should get \( y = 0 \).
4. Finding the y-intercept (b):
Let's generalize the equation of the new line as \( y = mx + b \). Since we know it intercepts the x-axis at \( x = 4 \):
[tex]\[ 0 = m \cdot 4 + b \][/tex]
Solving for \( b \):
[tex]\[ 0 = 4m + b \implies b = -4m \][/tex]
Now, substituting \( b = -4m \) back into the line equation \( y = mx + b \), we get:
[tex]\[ y = mx - 4m \][/tex]
However, when we rewrite the final equation, the standard way to express a line equation is simplified based on the given information. If our aim is to find \( x \)- and \( y \)-coordinates where \( y = 0 \):
The final simplified form of any line parallel to the original line with an \( x \)-intercept of 4 will point to \( y = 0 \).
The resulting equation based on these steps is:
[tex]\[ y = 0 \][/tex]
1. Equation of the original line:
The original line is provided in the standard form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
2. Parallel line characteristics:
Parallel lines have the same slope (\( m \)). Therefore, the new line will have the same slope as the original line.
3. Determining the new line's intercept:
For our new line with an \( x \)-intercept of 4, by definition, the \( x \)-intercept is the point where the line crosses the x-axis (\( y = 0 \)). Hence, if we substitute \( x = 4 \) into the line's equation, we should get \( y = 0 \).
4. Finding the y-intercept (b):
Let's generalize the equation of the new line as \( y = mx + b \). Since we know it intercepts the x-axis at \( x = 4 \):
[tex]\[ 0 = m \cdot 4 + b \][/tex]
Solving for \( b \):
[tex]\[ 0 = 4m + b \implies b = -4m \][/tex]
Now, substituting \( b = -4m \) back into the line equation \( y = mx + b \), we get:
[tex]\[ y = mx - 4m \][/tex]
However, when we rewrite the final equation, the standard way to express a line equation is simplified based on the given information. If our aim is to find \( x \)- and \( y \)-coordinates where \( y = 0 \):
The final simplified form of any line parallel to the original line with an \( x \)-intercept of 4 will point to \( y = 0 \).
The resulting equation based on these steps is:
[tex]\[ y = 0 \][/tex]
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.