Question

determine the equation of a line in slope-intercept parallel to 6x+2y=19 and passing through (-6,-13).

Answer 1

Answer:

$y = - 3x - 31$

Step-by-step explanation:

By definition, the slopes of parallel lines are equal. Thus, we need to first five the slope of 6x+2y=19. Recall that slope intercept form is

$y = mx + b$

where m is the slope and b is the y-intercept. So, to find the slope of 6x+2y=19, put it on slope intercept form like so:

6x+2y=19

6x-19=-2y

-3x+19/2=y

So the slope of the line is -3. Then, we will use point slope form to find the equation of the parallel line that passes through (-6, -13). Recall that point slope form is

y-y1=m(x-x1). Using this we find the equation of the parallel line to be:

y+13=-3(x+6)

y+13=-3x-18

y=-3x-31

Thus, the slope of the parallel line is y=-3x-31.

I hope this helps! Cheers!

Answer 2

Answer:  $y=-3x-31$

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

Given the equation:

$6x+2y=19$

You must solve for "y" in order to express it in Slope-Intercept form:

$2y=-6x+19\\\\y=-3x+\frac{19}{2}$

You can identify that:

$m=-3$

Since the slopes of parallel lines are equal, then the slope of the other line is:

$m=-3$

Then, you can substitute the slope and the coordinates of the given point into $y=mx+b$ and solve for "b":

$-13=-3(-6)+b\\\\-13-18=b\\\\b=-31$

Therefore, the equation of this line in Slope-Intercept form is:

$y=-3x-31$