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Applied Linear Equations 2


This topic continues the topic of Applied Linear Equations 1.
To review the Applied Linear Equations 1 topic, see here.

For two lines, where m1 is the slope of one line and m2 is the slope of the second line, the two lines are


Example 1: Perpendicular slope

What slope is perpendicular to slope 5/2?

To find the perpendicular slope, find the negative reciprocal of 5/2.
1. Flip the slope to get the reciprocal
5
2
  →   2
5
2. Reverse the sign to get the negative reciprocal
2
5
  →   - 2
5
The negative reciprocal of 5/2 is -2/5.

The answer is


Example 2: Find the equation of a line

In slope-intercept form, write the equation of the line that intersects (2, -4) and is perpendicular to x + 3y = 0
Equation:

1. Find the slope perpendicular to x + 3y = 0
A line equation with the form ax + by = c, the slope m = - a
b
The line x + 3y = 0 has a slope m = - 1
3
Therefore, the line perpendicular to x + 3y = 0 has a slope m1 = 3

2. Knowing the slope and intersection point, find the equation of the perpendicular line

The slope m1 = 3 and a point on the line (x, y) = (2, -4)
y = mx + b
-4 = 3(2) + b
-4 = 6 + b
-10 = b
Plugging the values for m and b into the slope-intercept formula, we get the answer

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