We have to determine the equation of the line passing through the point (2,-5) and parallel to the line [tex]5x = 6y+7[/tex]
When two lines are parallel, then the slopes of the two lines are equal.
Equation of line with point [tex](x_1, y_1)[/tex] and slope 'm' is given by:
[tex](y-y_1) = m(x-x_1)[/tex]
Since, we have to determine the equation of a line with point (2,-5).
So, the equation of the line is : [tex](y-(-5)) = m(x-2)[/tex]
[tex]y+5 = m(x-2)[/tex]
Since, the line is parallel to the line [tex]5x = 6y+ 7[/tex]
So, [tex]6y +7 = 5x[/tex]
[tex]6y = 5x - 7[/tex]
[tex]y = \frac{5}{6}x - \frac{7}{6}[/tex]
So, slope of the line 'm' is [tex]\frac{5}{6}[/tex].
Therefore, the equation of the line is:
[tex](y+5) = \frac{5}{6}(x-2)[/tex]
[tex]6y + 30 = 5x - 10[/tex]
[tex]6y - 5x = -10-30[/tex]
[tex]6y - 5x = -40[/tex]
Therefore, [tex]6y - 5x = -40[/tex] is the required equation of the line.
