Question

Choose the equation below that represents the line passing through the point (2, −5) with a slope of −3

Answer 1

`y = - 3x + 1`

or

`3x + y = 1`

Step-by-step explanation

The equation is calculated using the formula,

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

where m=-3 is the slope and

`(x_1,y_1) = (2, - 5)`

We substitute the the values to get:

`y- - 5= - 3(x-2)`

Expand

`y + 5= - 3x + 6`

`y = - 3x + 6 - 5`

`y = - 3x + 1`

This is the slope-intercept form.

Or in standard form;

`3x + y = 1`

Answer 2

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

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

Where:

m: It's the slope

`(x_ {0}, y_ {0}):`It is a point

We have to:

`m = -3\\(x_ {0}, y_ {0}): (2, -5)`

Substituting:
`y - (- 5) = - 3 (x-2)\\y + 5 = -3 (x-2)\\y + 5 = -3x + 6\\y = -3x+1`

ANswer:

`y + 5 = -3 (x-2)\\y = -3x+1`