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Stels [109]
3 years ago
13

In what form is the following linear equation written?

Mathematics
1 answer:
Masja [62]3 years ago
3 0

9514 1404 393

Answer:

  C.  Slope-intercept

Step-by-step explanation:

There are numerous forms of the equation of a line. Here are a few.

  y = mx + b . . . . slope-intercept form; slope m, y-intercept b

  y -k = m(x -h) . . . . point-slope form; point (h, k), slope m

  ax +by = c . . . . standard form; mutually prime integers, a > 0

  x/a +y/b = 1 . . . . intercept form; x-intercept a, y-intercept b

  ax +by +c = 0 . . . . general form

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1 . . . . two-point form; points (x1, y1), (x2, y2)

  (y2 -y1)/(x2 -x1) = (y -y1)/(x -x1) . . . . you might call this rise-run form

__

The given equation best matches slope-intercept form; slope 9, y-intercept 2.

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Answer:

Step-by-step explanation:

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3 years ago
Find the value of k so that 48x-ky=11 and (k+2)x+16y=-19 are perpendicular lines.
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Answer: k = -1 +/- √769

<u>Step-by-step explanation:</u>

48x - ky = 11

<u>-48x        </u>  <u> -48x</u>

         -ky = -48x + 11

         \frac{-ky}{-k} = \frac{-48x}{-k} + \frac{11}{-k}    

           y =\frac{48x}{k} - \frac{11}{k}

Slope: \frac{48}{k}

*************************************************************************

 (k + 2)x + 16y = -19

<u>- (k + 2)x          </u>   -<u>(k + 2)x </u>

                 16y = -(k + 2)x - 19

                  \frac{16y}{16} = -\frac{(k + 2)x}{16} - \frac{19}{16}

                  y = -\frac{(k + 2)x}{16} - \frac{19}{16}

Slope: -\frac{(k + 2)}{16}

**********************************************************************************

\frac{48}{k} and -\frac{(k + 2)}{16} are perpendicular so they have opposite signs and are reciprocals of each other.  When multiplied by its reciprocal, their product equals -1.

-\frac{(k + 2)}{16} *  \frac{k}{48} = -1

\frac{(k + 2)k}{16(48)} = 1

Cross multiply, then solve for the variable.

(k + 2)(k) = 16(48)

k² + 2k - 768 = 0

Use quadratic formula to solve:

k = -1 +/- √769



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