Question

What is an equation of the line that passes through the points (2,-1) and (3,-4)?

Answer 1

The equation of a line that passes through points (2, - 1) and (3, - 4) is

y = -3x + 5

Explanation:

In order to solve this we need to know the following slope formula

`m= (y_(2) - y_(1) )/(x_(2) - x_(1) )`

Where m is the slope

Now let (2,-1) be
`(x_(1) , y_(1) )`, and (3,-4) be
`(x_(2) , y_(2))`. So now we do....

`m= (y_(2) - y_(1) )/(x_(2) - x_(1) ) = (-4 + 1)/(3 - 2)= (-3)/(1) = - 3`

From here we can find the equation of this line by using the slope point form of an equation, and we will obtain the following......

`y - y_(1) = m(x - x_(1) )\\y + 1 = -3(x -2)\\y + 1= -3x + 6\\y = -3x + 5`