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Write the equation of a line that passes the point (-6,9)and is perpendicular to a line that passes through the points (-2,1) and (6,7).

Sagot :

rspill6

Answer:  y = -(4/3)x + 1

Step-by-step explanation:

Let's start with finding an equation of a straight line (y=mx+b) that goes through points (-2,1) and (6,7).

The slope of a line, m, is the change in y for the change in x, or Rise/Run.

This is derived from the two points.

Rise (7-1) = 6

Run (6 - (-2)) = 8

Rise/Run = 6/8 or 3/4

The line is therefore y = (3/4)x + b

Find b by using one of the two points.  I'll use (-2,1), but the other would also work.

y = (3/4)x + b

1 = (3/4)(-2) + b

1 = -(6/4) + b

b = 10/4

The line becomes y = (3/4)x + 10/4

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A line perpendicular to this will have a slope that is the negative inverse of the original line.  The negative inverse of (3/4) is -(4/3).

The perpendicular line will be:

y = -(4/3)x + b

Use point (-6,9) to find b:

y = -(4/3)x + b

9 = -(4/3)*(-6) + b

9 = (24/3) + b

b = (27/3 - 24/3) = 3/3 = 1

The line is y = -(4/3)x + 1

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