Welcome to Westonci.ca, your go-to destination for finding answers to all your questions. Join our expert community today! Discover in-depth solutions to your questions from a wide range of experts on our user-friendly Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
To determine the equation of the line that passes through the origin and is parallel to line [tex]\( AB \)[/tex], follow these steps:
1. Calculate the slope of line [tex]\( AB \)[/tex]:
The slope [tex]\( m \)[/tex] between two points [tex]\( (x_1, y_1) \)[/tex] and [tex]\( (x_2, y_2) \)[/tex] is calculated as:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Given points [tex]\( A(-3,0) \)[/tex] and [tex]\( B(-6,5) \)[/tex]:
[tex]\[ m = \frac{5 - 0}{-6 - (-3)} = \frac{5}{-6 + 3} = \frac{5}{-3} = -\frac{5}{3} \][/tex]
2. Determine the equation of the line parallel to [tex]\( AB \)[/tex] that passes through the origin:
A line parallel to [tex]\( AB \)[/tex] will have the same slope, [tex]\( m = -\frac{5}{3} \)[/tex]. The equation of a line through the origin (0,0) with slope [tex]\( m \)[/tex] can be written in slope-intercept form as:
[tex]\[ y = mx \][/tex]
Substituting [tex]\( m \)[/tex] gives:
[tex]\[ y = -\frac{5}{3}x \][/tex]
3. Rewrite in standard form (Ax + By = C):
Rearranging [tex]\( y = -\frac{5}{3}x \)[/tex] to standard form:
[tex]\[ \frac{5}{3}x + y = 0 \][/tex]
Multiply through by 3 to clear the fraction:
[tex]\[ 5x + 3y = 0 \][/tex]
After comparing with the given options, none of those options match exactly. Therefore, it indicates that none of the listed choices correctly matches our derived equation.
Thus, the correct answer is:
[tex]\[ \boxed{\text{None of the above}} \][/tex]
1. Calculate the slope of line [tex]\( AB \)[/tex]:
The slope [tex]\( m \)[/tex] between two points [tex]\( (x_1, y_1) \)[/tex] and [tex]\( (x_2, y_2) \)[/tex] is calculated as:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Given points [tex]\( A(-3,0) \)[/tex] and [tex]\( B(-6,5) \)[/tex]:
[tex]\[ m = \frac{5 - 0}{-6 - (-3)} = \frac{5}{-6 + 3} = \frac{5}{-3} = -\frac{5}{3} \][/tex]
2. Determine the equation of the line parallel to [tex]\( AB \)[/tex] that passes through the origin:
A line parallel to [tex]\( AB \)[/tex] will have the same slope, [tex]\( m = -\frac{5}{3} \)[/tex]. The equation of a line through the origin (0,0) with slope [tex]\( m \)[/tex] can be written in slope-intercept form as:
[tex]\[ y = mx \][/tex]
Substituting [tex]\( m \)[/tex] gives:
[tex]\[ y = -\frac{5}{3}x \][/tex]
3. Rewrite in standard form (Ax + By = C):
Rearranging [tex]\( y = -\frac{5}{3}x \)[/tex] to standard form:
[tex]\[ \frac{5}{3}x + y = 0 \][/tex]
Multiply through by 3 to clear the fraction:
[tex]\[ 5x + 3y = 0 \][/tex]
After comparing with the given options, none of those options match exactly. Therefore, it indicates that none of the listed choices correctly matches our derived equation.
Thus, the correct answer is:
[tex]\[ \boxed{\text{None of the above}} \][/tex]
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.