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.

  1. Slope in standard form is -A/B = 1/2

  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.

Want more practice questions? Check out the Worthington Prep SAT Tutoring Questions page.

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Q6. Slope