Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Get detailed answers to your questions from a community of experts dedicated to providing accurate information. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
To determine the point-slope equation of the line passing through the points [tex]\((-5, 7)\)[/tex] and [tex]\((-4, 0)\)[/tex], we'll follow these steps:
1. Identify the coordinates of the points:
[tex]\[ (x_1, y_1) = (-5, 7) \][/tex]
[tex]\[ (x_2, y_2) = (-4, 0) \][/tex]
2. Calculate the slope [tex]\( m \)[/tex] of the line:
The formula for the slope between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Substituting the given coordinates:
[tex]\[ m = \frac{0 - 7}{-4 - (-5)} = \frac{-7}{-4 + 5} = \frac{-7}{1} = -7 \][/tex]
3. Use the point-slope form of the equation of a line:
The point-slope form is written as:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Substituting [tex]\( m = -7 \)[/tex], [tex]\( x_1 = -5 \)[/tex], and [tex]\( y_1 = 7 \)[/tex]:
[tex]\[ y - 7 = -7(x + 5) \][/tex]
Here, we adjust the expression inside the parentheses to account for [tex]\( x_1 = -5 \)[/tex]:
[tex]\[ x - (-5) = x + 5 \][/tex]
Thus, the point-slope equation of the line through [tex]\((-5, 7)\)[/tex] and [tex]\((-4, 0)\)[/tex] is:
[tex]\[ y - 7 = -7(x + 5) \][/tex]
1. Identify the coordinates of the points:
[tex]\[ (x_1, y_1) = (-5, 7) \][/tex]
[tex]\[ (x_2, y_2) = (-4, 0) \][/tex]
2. Calculate the slope [tex]\( m \)[/tex] of the line:
The formula for the slope between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Substituting the given coordinates:
[tex]\[ m = \frac{0 - 7}{-4 - (-5)} = \frac{-7}{-4 + 5} = \frac{-7}{1} = -7 \][/tex]
3. Use the point-slope form of the equation of a line:
The point-slope form is written as:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Substituting [tex]\( m = -7 \)[/tex], [tex]\( x_1 = -5 \)[/tex], and [tex]\( y_1 = 7 \)[/tex]:
[tex]\[ y - 7 = -7(x + 5) \][/tex]
Here, we adjust the expression inside the parentheses to account for [tex]\( x_1 = -5 \)[/tex]:
[tex]\[ x - (-5) = x + 5 \][/tex]
Thus, the point-slope equation of the line through [tex]\((-5, 7)\)[/tex] and [tex]\((-4, 0)\)[/tex] is:
[tex]\[ y - 7 = -7(x + 5) \][/tex]
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.