write an equation of the line containing the given point and parallel to the given line (2,-4); 8x-3y=2 the equation of the line is y=

since it is parallel to 8x - 3y = 2, the new line will differ only in the constant.

let the new line be 8x - 3y = c
plug in the given point (2,-4)
16 + 12 = c = 28

8x - 3y = 28

figure slope first.

slope first: 3y=8x-2, or y= 8/2 x=2/3
slope is 2/3

Then, the line

y= mx+b
y= 8/3 x +b put in (2,-4), and solve for b, thence you have the line.

To determine the equation of a line parallel to the given line, we need to ensure that the slope of the new line is the same as the slope of the given line.

First, let's rearrange the given equation into slope-intercept form (y = mx + b), where m represents the slope:

8x - 3y = 2

To isolate y, we subtract 8x from both sides of the equation:

-3y = -8x + 2

Next, divide the entire equation by -3 to solve for y:

y = (8/3)x - 2/3

Since we want a line parallel to this, the slope will remain the same, which is 8/3.

Now we can use the point-slope formula to find the equation of the line passing through the given point (2, -4):

y - y₁ = m(x - x₁)

In this case, the point (x₁, y₁) = (2, -4), and the slope (m) = 8/3.

Substituting the values into the equation:

y - (-4) = (8/3)(x - 2)

Simplifying further:

y + 4 = (8/3)(x - 2)

This is the equation of the line parallel to 8x - 3y = 2, passing through the point (2, -4).

To find the equation of a line parallel to the given line containing the point (2, -4), we can use the fact that parallel lines have the same slope. Therefore, we need to find the slope of the given line and use it to write the equation of the new line.

First, let's rearrange the given line 8x - 3y = 2 into slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.

8x - 3y = 2
-3y = -8x + 2 (Subtract 8x from both sides)
y = (8/3)x - 2/3 (Divide by -3)

Now that we have the slope-intercept form, we can see that the slope of the given line is 8/3. Since we want the new line to be parallel, it should have the same slope.

So, the equation of the line parallel to 8x - 3y = 2 containing the point (2, -4) can be written as:

y = (8/3)x + b

Now, we need to find the value of b (the y-intercept) using the given point (2, -4).

Substitute the coordinates x = 2 and y = -4 into the equation:

-4 = (8/3)(2) + b

Simplifying:

-4 = 16/3 + b (Multiply 8/3 by 2)
-4 - 16/3 = b (Subtract 16/3 from both sides)
-12/3 - 16/3 = b (Convert -4 to a fraction with the same denominator)
-28/3 = b

Therefore, the equation of the line parallel to 8x - 3y = 2 containing the point (2, -4) is:

y = (8/3)x - 28/3