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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]
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