Considering the definition of perpendicular line, the equation of of perpendicular line is y=2x -1.
<h3>Linear equation</h3>
A linear equation o line can be expressed in the form y = mx + b
where
- x and y are coordinates of a point.
- m is the slope.
- b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.
<h3>Perpendicular line</h3>
Perpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.
<h3>Equation of perpendicular line in this case</h3>
The line is y= -1/2x+5
If you multiply the slopes of two perpendicular lines, you get –1. In this case, the line has a slope of -1/2. So:
-1/2× slope perpendicular line= -1
slope perpendicular line= (-1)÷ (-1/2)
<u><em>slope perpendicular line= 2</em></u>
So, the perpendicular line has a form of: y= 2x + b
The line passes through the point (-2, -5). Replacing in the expression for perpendicular line:
-5= 2×(-2) + b
-5= -4 + b
-5 +4= b
<u><em>-1= b</em></u>
Finally, the equation of of perpendicular line is y=2x -1.
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