Question

Equation of line that passes through points (6,-1) and is parallel to the line 5x+6y=6?

Answer 1

`y + 1 = -(5)/(6)(x-6)`

or

`y = -(5)/(6)x +4`

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.

`y-y_1=m(x-x_1)\\y --1 = -(5)/(6)(x - 6)\\y + 1 = -(5)/(6)(x-6)`

Convert the equation to slope intercept form by applying the distributive property.

`y + 1 = -(5)/(6)(x-6)\\y + 1 = -(5)/(6)x +5\\y = -(5)/(6)x +5-1\\y = -(5)/(6)x +4`