Q7. Perpendicular lines
Question
The equation of line 1 is x - 2y = 3. Which of the following is an equation of the line that is perpendicular to line I?
a) y = x + 2
b) y = -x + 2
c) Y = 2x - 1
d) Y = -2x + 1
Explanation
This equation is in the standard form Ax + By = C. We have 2 options to figure out the slope.
Slope in standard form is -A/B = 1/2
Convert to slope-intercept form.
x - 2y = 3
2y = x - 3;
y = 1/2x - 3/2
Slope = 1/2
Slope of a perpendicular line to this one would be -2 (negative reciprocal).
The only equation above that has a slope of -2 is D.
Lesson
Two lines are perpendicular if their slopes are opposite reciprocals, i.e., the product of their slopes is -1.
Two different lines are parallel if their slopes are equal but they are not the same line.
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