On a coordinate plane, a line goes through (negative 8, 4) and (8, 4). A point is at (negative 4, negative 6). What is the equation of the line that is parallel to the given line and passes through the point (−4,−6 )?

x = −6
x = −4
y = −6
y = −4

The equation of parallel line passes through the point (−4,−6 ) is:

y = -6

Please also check the attached graph.

Step-by-step explanation:

The slope-intercept form of the line equation

y = mx+b

where

Given that on a coordinate plane passes through (-8, 4) and (8, 4).

As the value of y remains the same for any value of x.

i.e. y = 4 for any value of x.

Thus, the given line is a horizontal line.

We know that the slope of a horizontal line is zero.

Also it is clear that at x = 0, the value of y = 4. In other words, we can observe that the y-intercept b = 4.

so substitutig m = 0 and b = 4 in the slope-intercept form

y = mx + b

y = 0x + 4

y = 4

Therefore, the equation of line passing through the point  (-8, 4) and (8, 4) is:

y = 4

Now, we also know that the slope of parallel lines is equal.

Thus, the slope of the line parallel to the line y = 4 is also 0.

As the parallel line passes through (−4,−6 ).

so substituting m = 0 and (-4, -6) in the slope-intercept form of line equation to determine the y-intercept b

y = mx + b

(-6) = 0(-4) + b

-6 = 0 + b

switching the sides

0 + b = -6

b = -6

Thus, the slope-intercept b = -6

now substituting m = 0 and b = -6 in the slope-intercept form of line equation

y = mx + b

y = 0(x) + -6

y = 0 - 6

y = -6

Therefore, the equation of parallel line passes through the point (−4,−6 ) is:

y = -6

Please also check the attached graph.