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

Question

asked Jul 6, 2020 141k views

1 Answer

KirkoR · Answer 1 · 2020-07-10T17:58:53+0000

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:

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