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

Answer:

$y=-7x-11$

Step-by-step 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:

$Slope,m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Here, $x_{1}=-2,y_{1}=3,x_{2}=-1,y_{2}=-4$

∴ $m=\frac{-3-4}{-1-(-2)}=\frac{-7}{-1+2}=\frac{-7}{1}=-7$

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,

$y-3=-7(x-(-2))\\y-3=-7(x+2)\\y-3=-7x-(7\times 2)\\y-3=-7x-14\\y=-7x-14+3\\y=-7x-11$

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