Answer:
[tex]y + 1 = -\frac{5}{6}(x-6)[/tex]
or
[tex]y = -\frac{5}{6}x +4[/tex]
Step-by-step explanation:
Parallel lines are lines which have the same slope. To write the equation of the line parallel, find the slope of the equation 5x + 6y = 6 through conversion into slope intercept form.
5x + 6y = 6 becomes y = -5/6x + 1. The slope is -5/6.
Substitute\ m =-5/6 and the point (6,-1) into the slope intercept form.
[tex]y-y_1=m(x-x_1)\\y --1 = -\frac{5}{6}(x - 6)\\y + 1 = -\frac{5}{6}(x-6)[/tex]
Convert the equation to slope intercept form by applying the distributive property.
[tex]y + 1 = -\frac{5}{6}(x-6)\\y + 1 = -\frac{5}{6}x +5\\y = -\frac{5}{6}x +5-1\\y = -\frac{5}{6}x +4[/tex]
