Question

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

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:

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

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

Answer 2

Answer:

y + 5 = -3 (x-3)

Option D

Step-by-step explanation: