Question

Parallel to 6x+5y= -5 and passes through the point (5,-4)

Answer 1

For this case we have that by definition, the equation of the line in the slope-intersection form is given by:

`y = mx + b`

Where:

m: It's the slope

b: It is the cut-off point with the y axis

We have the following equation:

`6x + 5y = -5\\5y = -6x-5\\y = - \frac {6} {5} x- \frac {5} {5}\\y = - \frac {6} {5} -1`

Thus, the slope is:
`m = - \frac {6} {5}`

By definition, if two lines are parallel then their slopes are equal.

Thus, a line parallel to the given line will have a slope:
`m = - \frac {6} {5}.`Therefore, the equation will be of the form:

`y = - \frac {6} {5} x + b`

We substitute the given point and find "b":

`-4 = - \frac {6} {5} (5) + b\\-4 = -6 + b\\-4 + 6 = b\\b = 2`

Finally, the equation is:

`y = - \frac {6} {5} x + 2`

Answer:

`y = - \frac {6} {5} x + 2`