Question

A line passes through the points (-6,4) and (-2,2). Which is the equation of the line?

Answer 1

The answer is y= -1/2x + 1

Answer 2

Answer:

The equation of the line is $y=\frac{-1}{2}x+1$

Step-by-step explanation:

1. The equation of the line that passes through two points can be expresed as:

$\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}$ (Eq.1)

where $x_{1}$, $x_{2}$, $y_{1}$ and $y_{2}$ are the given points.

2. Name the points:

$x_{1}$=-6

$x_{2}$=-2

$y_{1}$=4

$y_{2}$=2

3. Replace the points in the Eq.1:

$\frac{y-4}{x-(-6)}=\frac{2-4}{-2-(-6)}$

$\frac{y-4}{x+6}=\frac{2-4}{-2+6}$

$\frac{y-4}{x+6}=\frac{-2}{4}$

$\frac{4(y-4)}{x+6}=-2$

$4(y-4)=-2(x+6)$

$4y-16=-2x-12$

$4y=-2x-12+16$

$4y=-2x+4$

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

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

$y=\frac{-1}{2}x+1$