Answer: y = (-1/2)x + 2
Concept:
When two lines are perpendicular to each other, their slopes are negative reciprocals.
The reciprocal of a number is 1 divided by the number.
In other words, it is the image opposite of a term.
Solve:
Given information
Given line = y = 2x - 5
Point = (-4, 4)
Find the slope of the line
Given the line is perpendicular to the line y = 2x - 5, the slope of the line would be negative reciprocal of the line y = 2x - 5.
Slope of line [y = 2x - 5] = 2
Slope of new line = (-1/2)
Find the y-intercept by substituting the given point
Equation of the new line: y = (-1/2)x + b
y = (-1/2)x + b
4 = (-1/2) (-4) + b
4 = 2 + b
4 - 2 = 2 + b - 2
b = 2
Finalize the equation of the line
Slope = -1/2
Y-intercept = 2
[tex]\boxed{y=-\frac{1}{2}x+2 }[/tex]
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