Algebra unit 6 retake

Which equation of a line is perpendicular to the equation -4 + 3y = 12

y= 3x×2
y= -3/4 x + 6
y= 4/3 x + 6
y=4x+8

1 answer

To find an equation of a line that is perpendicular to the given equation \(-4 + 3y = 12\), we first need to rewrite this equation in slope-intercept form (i.e., \(y = mx + b\)), where \(m\) is the slope.

  1. Rearranging the given equation:

    \[ -4 + 3y = 12 \]

    We can add 4 to both sides:

    \[ 3y = 16 \]

    Now, divide by 3:

    \[ y = \frac{16}{3} \]

    Since this line is horizontal, its slope is \(0\).

  2. Finding the slope of the perpendicular line:

    The slope of a line that is perpendicular to another line is the negative reciprocal of the original slope. However, since we have a horizontal line (slope of \(0\)), the slope of the perpendicular line will be undefined, which corresponds to a vertical line.

  3. Looking at the choices for vertical lines:

    None of the options listed represent vertical lines. Let's break down each option to find the slope:

  • \(y = 3x \times 2\) or \(y = 6x\) (slope = 6)
  • \(y = -\frac{3}{4}x + 6\) (slope = -\(\frac{3}{4}\))
  • \(y = \frac{4}{3}x + 6\) (slope = \(\frac{4}{3}\))
  • \(y = 4x + 8\) (slope = 4)

Since none of the options represent a vertical line, it seems that none of them is correct for being perpendicular to the original horizontal line.

Conclusion: There is no provided option that correctly represents a line perpendicular to the initial equation of a horizontal line. A perpendicular line would be vertical, which is not included in your choices.