Find the equation for the line below

  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

_____

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

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

Doing this, we get that the the equation of the line is:

Equation of a line:

The equation of a line is given by:

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:

Thus:

Intercept:

We apply one one the points, I am going to apply (2,-4), that is, when . With this, we find the intercept. So

Thus, the equation of the line is:

A similar question is given at link