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

Third option:
`y=-3(x-4)`

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=(y_2-y_1)/(x_2-x_1)`

Substituting values, we get:

`m=(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