Question

Use the coordinates of the labeled point to find the point-slope equation of the line.

Answer 1

y + 5 = -3 (x-3)

Option D

Explanation:

Answer 2

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}): (3, -5)\\(x_ {2}, y_ {2}): (0,4)\\m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {4 - (- 5)} {0-3} = \frac {4 + 5} {-3} = \frac {9} {- 3} = - 3`

Thus, the equation is of the form:

`y-y_ {0} = - 3 (x-x_ {0})`

We choose a point:

`(x_(0), y_ {0}) :( 3, -5)`

Finally, the equation is:

`y - (- 5) = - 3 (x-3)\\y + 5 = -3 (x-3)`

Answer:

`y + 5 = -3 (x-3)`

Option D