Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
To complete the point-slope equation of the line through the points [tex]\((-5, 7)\)[/tex] and [tex]\((-4, 0)\)[/tex], let's go through the steps in detail:
1. Identify the points: We are given the points [tex]\((-5, 7)\)[/tex] and [tex]\((-4, 0)\)[/tex].
2. Determine the slope:
- The formula for the slope [tex]\( m \)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
- Substituting our points:
[tex]\[ m = \frac{0 - 7}{-4 - (-5)} = \frac{-7}{-4 + 5} = \frac{-7}{1} = -7 \][/tex]
3. Write the point-slope form equation:
- The point-slope form of a line equation is given by:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
- Here, [tex]\( (x_1, y_1) = (-5, 7) \)[/tex] and [tex]\( m = -7 \)[/tex].
4. Substitute the known values into the equation:
[tex]\[ y - 7 = -7(x - (-5)) \][/tex]
5. Simplify the equation:
- Since [tex]\( x - (-5) \)[/tex] simplifies to [tex]\( x + 5 \)[/tex]:
[tex]\[ y - 7 = -7(x + 5) \][/tex]
Therefore, the complete point-slope equation of the line is:
[tex]\[ y - 7 = -7(x + 5) \][/tex]
1. Identify the points: We are given the points [tex]\((-5, 7)\)[/tex] and [tex]\((-4, 0)\)[/tex].
2. Determine the slope:
- The formula for the slope [tex]\( m \)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
- Substituting our points:
[tex]\[ m = \frac{0 - 7}{-4 - (-5)} = \frac{-7}{-4 + 5} = \frac{-7}{1} = -7 \][/tex]
3. Write the point-slope form equation:
- The point-slope form of a line equation is given by:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
- Here, [tex]\( (x_1, y_1) = (-5, 7) \)[/tex] and [tex]\( m = -7 \)[/tex].
4. Substitute the known values into the equation:
[tex]\[ y - 7 = -7(x - (-5)) \][/tex]
5. Simplify the equation:
- Since [tex]\( x - (-5) \)[/tex] simplifies to [tex]\( x + 5 \)[/tex]:
[tex]\[ y - 7 = -7(x + 5) \][/tex]
Therefore, the complete point-slope equation of the line is:
[tex]\[ y - 7 = -7(x + 5) \][/tex]
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.