Question

What is the equation for the line? Enter your answer in the box. Graph of a line on a coordinate plane. The horizontal x axis ranges from negative 10 to 10 in increments of 2. The vertical y axis ranges from negative 10 to 10 in increments of 2. A line passes through points begin ordered pair negative 4 comma 4 end ordered pair and begin ordered pair negative 2 comma 0 end ordered pair and begin ordered pair 0 comma negative 4 end ordered pair and begin ordered pair 2 comma negative 8 end ordered pair.

Answer 1

Equation of line passing through two points $(x_{1},y_{1}), and (x_{2},y_{2}) is$=$\frac {y-y_{1}}{x-x_{1}}=\frac{y_{2} - y_{1}}{ x_{2}-x_{1}}$

Now , we will find first equation of line which passes through (-4,4) and  (-2,0) is :

$\frac{y-4}{x+4}= \frac{0-4}{-2+4}\\\\\frac{y-4}{x+4}= \frac{-4}{2}\\\\y-4 = -2 x -8\\\\y +2 x +4=0$

The Second line which passes through (0,-4) and (2,-8) is :

$\frac{y+4}{x-0}= \frac{-8+4}{2-0}\\\\\frac{y+4}{x}= \frac{-4}{2}\\\\y+4 = -2 x \\\\y +2 x +4=0$

So equation of line passing through (-4,4) , (-2,0) ,(0,-4) and (2,-8) is :(All points are collinear, so there will be unique line passing through these four points.)

2 x + y + 4=0