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 · 2021-10-05T11:12:21+02:00

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

The slope of a horizontal line is zero.

Slopes of two parallel lines are same.

So, the slope of the required line is [tex]0[/tex].

The required line passes through the point [tex](-4,-6)[/tex].

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

Substitute [tex]m=0, y_1=-6[/tex] and [tex]x_1=-4[/tex] in the above equation.

[tex]y-(-6)=0(x-(-4))[/tex]

[tex]y+6=0[/tex]

[tex]y=-6[/tex]

Therefore the equation of required line is [tex]y=-6[/tex].

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