Question

The slope of the line below is -2. Write the point-slope equation of the line

Answer 1

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

$y-y_{0}=m(x-x_{0})$

Where:

m: It is the slope of the line

$(x_ {0}, y_ {0})$: It is a point through which the line passes.

We have to:

$m = -2$

Thus, the equation is of the form:

$y-y_{0}=-2(x-x_{0})$

We substitute the point $(x_{0}, y_{0}) :( 4, -6)$

$y-(-6)=-2(x-4)\\y+6=-2(x-4)$

Finally, the equation is:

$y+6=-2(x-4)$

Answer:

$y = -2x + 2$

$y+6=-2(x-4)$