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)

kobenhavn kobenhavn · Answer 2 · 2021-10-05T05:12:21-04:00

The equation of line that is parallel to the given line and passes through the point \((-4,-6)\) is \(y=-6\).

The slope of a horizontal line is zero.

Slopes of two parallel lines are same.

So, the slope of the required line is \(0\).

The required line passes through the point \((-4,-6)\).

The point slope form of a line is \(y-y_1=m(x-x_1)\), where, \(m\) is the slope.

Substitute \(m=0, y_1=-6\) and \(x_1=-4\) in the above equation.

\(y-(-6)=0(x-(-4))\)

\(y+6=0\)

\(y=-6\)

Therefore the equation of required line is \(y=-6\).

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