What is the equation of the line that is parallel to the given line and passes through the point (−4,−6 )?

First you'll have to find the slope of your given points -- but i'll save you the time and let you know that the slope is 0. y2 - y1 in this case would be (4 - 4), aka 0. if you have a slope of 0, your line will be horizontal.

so a line that passes through (-4, -6) that is parallel with a horizontal line will have to be a horizontal line as well. all you have to do is take the y-value of that point and turn it into a y = mx + b equation:

y = -6

that satisfies both requirements -- it passes through (-4, -6) and is parallel with the line y = 4 (y = 4 is the line you get from the given points)