Write an equation for the line parallel to the line - 8x + 4y = 4 through the point (-6,3). Please enter your answer in slope intercept form or standard form.

To find the equation for the line parallel to the line -8x + 4y = 4, passing through the point (-6,3), we will first make the equation given to be in slope-intercept form, so that we can find the slope of this line

-8x + 4y = 4 we have to change it to the form y=mx + c

To do that, lets add 8x to both-side of the equation

8x -8x +4y=8x+4

4y=8x+4

divide both-side of the equation by 4

4y/4 = 8x/4 +4/4

y=2x + 1

comparing the above equation with y=mx + c

our slope(m) = 2

Any equation parallel to this line will have the same slope, so the slope(m) of our new equation will also be 2

Now we need to find the intercept of our new equation, to do that we will plug in the points given and our new slope into y=mx + c and find the value of our intercept(c)

The points given are x=-6 and y=3 and our new slope is m=2

plugging in our variables, thus;

y =mx + c

3 = 2(-6) + c

3 = -12 + c

add 12 to both-side of the equation

3+12 = -12+12+c

15=c

c=15

Therefore our intercept for the new equation is 15

To form our new equation, we will just plug in our new slope and intercept into y=mx + c

y = 2x + 15 (this is in slope intercept form)

we can rearrange it to be in standard form;

2x- y-15=0