Question

What is the equation in point-slope form of the line passing through (4, 0) and (2, 6)? (5 points) y = 4x − 2 y = 2x − 4 y = −3(x − 4) y = 3(x + 4)

Answer 1

Answer:

Third option:  $y=-3(x-4)$

Step-by-step explanation:

The equation of the line in Point-Slope form is:

$y-y_1=m(x-x_1)$

Where "m" is the slope and $(x_1,y_1)$ is a point on the line.

Given the points  (4, 0) and (2, 6), we can find the slope with this formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

Substituting values, we get:

 $m=\frac{0-6}{4-2}=-3$

Finally, substituting the slope and the point (4,0) into  $y-y_1=m(x-x_1)$, we get:

 $y-0=-3(x-4)$

 $y=-3(x-4)$

Answer 2

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

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

We have the following points:

$(x_ {1}, y_ {1}) :( 2,6)\\(x_ {2}, y_ {2}) :( 4,0)\\m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {0-6} {4-2} = \frac {-6} {2} = -3$

We chose a point:

$(x_ {0}, y_ {0}) :( 4,0)$

Substituting in the equation we have:

$y-0 = -3 (x-4)\\y = -3 (x-4)$

Finally, the equation is: $y = -3 (x-4)$

Answer:

OPTION C