Question

What is the equation of the following line written in slope-intercept form -2/3 and -1/-4? y = -11x - 7 y = -7x + 11 y = -7x - 11

Answer 1

`y=-7x-11`

Explanation:

Given:

The two points on the line are
`(-2,3)` and
`(-1,-4)`.

The slope of the line joining two points
`(x_(1),y_(1))` and
`(x_(2),y_(2))` is given as:

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

Here,
`x_(1)=-2,y_(1)=3,x_(2)=-1,y_(2)=-4`

∴
`m=(-3-4)/(-1-(-2))=(-7)/(-1+2)=(-7)/(1)=-7`

Equation of line with a point
`(x_(1),y_(1))` and slope
`m` is given as:

`y-y_(1)=m(x-x_(1))`

Plug in -2 for
`x_(1)`, 3 for
`y_(1)` and -7 for
`m`. This gives,

`y-3=-7(x-(-2))\\y-3=-7(x+2)\\y-3=-7x-(7* 2)\\y-3=-7x-14\\y=-7x-14+3\\y=-7x-11`

Therefore, the equation of the line in vertex form is
`y=-7x-11`.