Question

The given line passes through the points (-4, -3) and (4,

1)
What is the equation, in point-slope form, of the line that is
perpendicular to the given line and passes through the
point (-4, 3)?
Oy-3 = -2(x + 4)
4
3
2
(4,1)
Oy-3 = -2(x +4)
Ov-3 = {(x + 4)
Oy-3 = 2(x + 4)
+7
-321
2 3 4
5
X
2
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Answer 1

The equation of the line perpendicular to the given line and passing through (-4, 3) is (Y - 3) = -2(x + 4).

Step-by-step explanation:

To find the equation of the line that is perpendicular to the given line and passes through the point (-4, 3), we need to determine the slope of the given line. The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line.

The given line passes through the points (-4, -3) and (4, 1), so the slope of the given line is (1 - (-3))/(4 - (-4)) = 4/8 = 1/2.

Therefore, the slope of the perpendicular line is -2 (negative reciprocal of 1/2), and the equation of the line in point-slope form is(Y - 3) = -2(x + 4).

Answer 2

y = 2x + 11

Step-by-step explanation:

The first thing we need to do

is to find the slope of the line that passes through the points (-4,-3) and (4,1)

Mathematically, that would be;

m = y2-y1/(x2-x1)

where (x1,y1) = (-4,-3) and (x2,y2) = (4,1)

substituting these. values we have;

m = (1-(-3))/(4-(-4)) = 4/8 = 1/2 or 0.5

Now we are told this line is perpendicular to another line that passes through another point.

We can find the slope of this other line

Since both lines are perpendicular, the product of their slope is -1.

Thus , -0.5 * m = -1

m = -1/-0.5 = 2

So the slope of the other line is 2

Using the point-slope form;

y-y1= m(x-x1)

The point for the other line is (-4,3)

So the equation will be

y-3 = 2(x+4)

y-3 = 2x + 8

y = 2x + 11