Question

which equation describes the line that passes through the point (-4,-8) and is parallel to the line represented by the equation 7x - 2y = 8

Answer 1

The equation of the line parallel to the line represented by 7x - 2y = 8 and passing through (-4,-8) is y = (7/2)x + 6.

Step-by-step explanation:

To find the equation of a line parallel to the line represented by the equation 7x - 2y = 8 and passing through the point (-4,-8), we need to find the slope of the given line and then use that slope along with the coordinates of the given point in the point-slope form of a linear equation.

The given equation can be rearranged to the slope-intercept form y = mx + b, where m is the slope. Solving for y gives us:

7x - 2y = 8

-2y = -7x + 8

y = (7/2)x - 4

From this equation, we can see that the slope of the given line is 7/2.

Now, we can use the point-slope form of a linear equation to find the equation of the line parallel to the given line and passing through the point (-4,-8). The point-slope form is:

y - y1 = m(x - x1)

Plugging in the values for the point and the slope, we get:

y - (-8) = (7/2)(x - (-4))

y + 8 = (7/2)(x + 4)

y + 8 = (7/2)x + 14

y = (7/2)x + 14 - 8

y = (7/2)x + 6

Therefore, the equation of the line parallel to the given line and passing through the point (-4,-8) is y = (7/2)x + 6.

Answer 2

The equation is;

2y = 7x + 12

Step-by-step explanation:

General equation form is ;

y = mx + b

where m is slope and b is y-intercept

Let us rewrite the first equation;

2y = 7x - 8

y = 7x/2 - 4

the slope here is 7/2

If two lines are parallel, their slopes are equal

so we use the point-slope form to get the second equation

y-y1 = m(x-x1)

(x1,y1) = (-4,-8)

Thus, we have

y + 8 = 7/2(x + 4)

2y + 16 = 7x + 28

2y = 7x + 12