Respuesta :

sqdancefan

Answer:

  y = (-4/3)(x +4) +4

Step-by-step explanation:

Between the given points, the "rise" is -8 and the "run" is 6. The rise/run ratio is then -8/6 = -4/3. So, a version of the point-slope equation can be written:

  y = m(x -h) +k . . . . . . . line with slope m through point (h, k)

  y = (-4/3)(x +4) +4

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Comment on the answer

The image asks for "an equation", which seems to allow for any equation format. The equation shown above can be put into other forms.

  y -4 = -4/3(x +4) . . . . different point-slope form

  y = -4/3x -4/3 . . . . . . slope-intercept form

  4x +3y = -4 . . . . . . . . standard form

  4x +3y +4 = 0 . . . . . . general form

  x/(-1) +y/(-4/3) = 1 . . . . intercept form

Ver imagen sqdancefan

We have to find the equation of the line. To do this:

  • First, I will explain the standard equation of a line.
  • Then, we find the slope.
  • Finally, we find the y-intercept.

Doing this, we get that the the equation of the line is: [tex]y = -\frac{4}{3}x - \frac{4}{3}[/tex]

Equation of a line:

The equation of a line is given by:

[tex]y = mx + b[/tex]

In which m is the slope and b is the y-intercept.

Slope:

We have these two points: (-4,4) and (2,-4).

Given two points, the slope is given by the change in y divided by the change in x.

Change in x: 2 - (-4) = 2 + 4 = 6

Change in y: -4 - 4 = -8

Slope: [tex]m = -\frac{8}{6} = -\frac{4}{3}[/tex]

Thus:

[tex]y = -\frac{4}{3}x + b[/tex]

Intercept:

We apply one one the points, I am going to apply (2,-4), that is, when [tex]x = 2, y = -4[/tex]. With this, we find the intercept. So

[tex]y = -\frac{4}{3}x + b[/tex]

[tex]-4 = -\frac{4}{3}(2) + b[/tex]

[tex]b = \frac{8}{3} - 4[/tex]

[tex]b = \frac{8}{3} - \frac{12}{3}[/tex]

[tex]b = -\frac{4}{3}[/tex]

Thus, the equation of the line is:

[tex]y = -\frac{4}{3}x - \frac{4}{3}[/tex]

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