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

Use the coordinates of the labeled point to find the point-slope equation of the line-example-1

2 Answers

7 votes

Answer:

y + 5 = -3 (x-3)

Option D

Explanation:

User Ramon Bakker
by
7.7k points
4 votes

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

User RaZik
by
8.7k points

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