Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Experience the convenience of getting reliable answers to your questions from a vast network of knowledgeable experts. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
Solution:
The slope-intercept form of a line with slope m and y-intercept b is given by the following equation:
[tex]y\text{ = mx+b}[/tex]now, if the line that contains the point (-1,-2) is parallel to the line 5x+7y=12, then it has the same slope as this line, that is, the wanted line has the same slope as the line with equation 5x+7y=12. To find this slope, we must transform the equation 5x+7y=12 in the slope-intercept form:
[tex]7y\text{ = -5x +12}[/tex]solving for y, this is equivalent to:
[tex]y\text{ = -}\frac{5}{7}\text{x +}\frac{12}{7}[/tex]thus, the wanted line has the following slope:
[tex]m\text{ = -}\frac{5}{7}[/tex]then, the provisional equation for this line is:
[tex]y\text{ = -}\frac{5}{7}x+b[/tex]We only have to find the y-intercept. To achieve this, we must replace in the previous equation the coordinates of a point that belongs to the line and then solve for b. In this case, we can take the point (x,y)= (-1,-2), and we obtain:
[tex]-2\text{ = -}\frac{5}{7}(-1)+b[/tex]this is equivalent to:
[tex]-2\text{ = }\frac{5}{7}+b[/tex]solving for b, we get:
[tex]b\text{ = -2-}\frac{5}{7}\text{ =-}\frac{19}{7}[/tex]so that, we can conclude that the correct answer is:
[tex]y\text{ = -}\frac{5}{7}x-\frac{19}{7}[/tex]
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.
