Question

What is the slope-intercept equation of the line that is perpendicular to y-4=-2/3(x-6) and that passes through (-2, -2)?

Answers

  1. Answer:

    The slope-intercept equation is:

    y=\frac{3}{2}x+1

    Step-by-step explanation:

    Given the equation

    y-4=-\frac{2}{3}\left(x-6\right)

    comparing it with the point-slope form of the line equation

    y-y_1=m\left(x-x_1\right)

    where m is the slope

    • so the slope of the line is -2/3.

    As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line, so

    The slope of the perpendicular line will be: 3/2

    The point-slope form of the equation of the perpendicular line that goes through (-2, -2) is:

    y-y_1=m\left(x-x_1\right)

    y-\left(-2\right)=\frac{3}{2}\left(x-\left(-2\right)\right)

    y+2=\frac{3}{2}\left(x+2\right)

    writing the line equation in the slope-intercept form

    y+2=\frac{3}{2}\left(x+2\right)

    subtract 2 from both sides

    y+2-2=\frac{3}{2}\left(x+2\right)-2

    y=\frac{3}{2}x+1

    Thus, the slope-intercept equation is:

    y=\frac{3}{2}x+1

    Here,

    As the slope-intercept form is

    y=mx+b

    where m is the slope and b is the y-intercept

    so

    y=\frac{3}{2}x+1

    m=3/2

    b = y-intercept = 1

    Therefore, the slope-intercept equation is:

    y=\frac{3}{2}x+1

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