Question

Use the point and the slope to graph each line. Write the equation of the line. The line contains point (2, –2) and is perpendicular to a line with slope –1.

Answers

  1. Answer:

    y = x – 4

    Step-by-Step Explanation:

    Perpendicular lines have slopes that are negative reciprocals—multiplying their slopes result in -1.

    Given the slope of a line m = -1, then it means that the slope of the other line must be 1 (because multiplying the slope of line 1  (m1 = -1), and the slope of the other line (m2 = 1) results in: -1 × 1 = -1).

    Therefore, given the slope of line 2 (m2 = 1), and the point (2, -2), we could plug these values into the slope-intercept form and solve for the y-intercept (b):

    y = mx + b

    -2 = 1(2) + b

    -2 = 2 + b

    Subtract 2 from both sides to solve for b:

    -2 – 2 = 2 – 2 + b

    -4 = b

    Therefore, the y-intercept (b) = -4.

    Hence, the equation of the perpendicular line is: y = x – 4

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