Question

Which equation is a point slope form equation for line AB ?

y+2=−2(x−5)
y+6=−2(x−1)
y+1=−2(x−6)
y+5=−2(x−2)

Answer 1

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

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

Where:

m: It's the slope

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

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

`(x_ {1}, y_ {1}): (1,6)\\(x_ {2}, y_ {2}): (5, -2)\\m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-2-6} {5-1} = \frac {-8} {4} = -2`

Thus, the equation is of the form:

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

We choose a point:

`(x_(0), y_ {0}) :( 5, -2)`

Finally, the equation is:

`y - (- 2) = - 2 (x-5)\\y + 2 = -2 (x-5)`

Answer:

`y + 2 = -2 (x-5)`