Question

What is the equation of the lines that passes through the points (-2, -3) and (4, -5)?

A) y= -1/3x-3
B) y= -4x-11/3
C) y= 4x+3
D) y= -1/3x-11/3

Answer 1

Since all the options are in the slope intercept form, we find the equation using the formula,


`y = mx + c`
We can find m, the slope using the formula,


`m = ( change \: in \: y )/(change \: in \: x)`

`m = ( - 5 - - 3)/(4 - - 2)`

`m = ( - 2)/(6) = - (1)/(3)`

On substitution,


`y = - ( 1)/(3) x + c`

We use any of the points, say (-2,-3) to determine the value of c.


`- 3 = - (1)/(3) ( - 2) + c`

`c = - (11)/(3)`

The equation is therefore,


`y = - (1)/(3) x - (11)/(3)`

The correct answer is D.