Question

what is the equation of this graphed line? (2,6)(-4,-6)​

Answer 1

For this case we have that by definition, the equation of the line of the slope-intersection form is given by:

$y = mx + b$

Where:

m: It's the slope

b: It is the cut-off point with the y axis

To find the slope we need two points through which the line passes, according to the image we have the following points:

$(x_ {1}, y_ {1}) :( 2,6)\\(x_ {2}, y_ {2}): (- 4, -6)$

The slope is given by:

$m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-6-6} {- 4-2} = \frac {-12} {- 6} = 2$

Thus, the equation is of the form:

$y = 2x + b$

We found "b" replacing one of the points:

$6 = 2 (2) + b\\6 = 4 + b\\b = 6-4\\b = 2$

Finally, the equation is of the form:

$y = 2x + 2$

ANswer:

$y = 2x + 2$