Question

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

Answer 1

$m = \frac{2 - 4}{ - 2 + 6} \\ \frac{ - 2}{4} = \frac{ - 1}{2} \\ y - 2 = \frac{ - 1}{2} (x + 2) \\ y - 2 = - \frac{1}{2} x - 1 \\ y = - \frac{1}{2} x + 1$

Answer 2

Answer:

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

Step-by-step explanation:

The equation of a line is $y=mx+b$ where m is the pending and b is the y intercept,

First we are going to calculate m:

If you have two points $A=(x_{1},y_{1})\\B=(x_{2},y_{2})$,

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

Now we have, A=(-6,4) and B=(-2,2),

$x_{1}=-6 , y_1=4\\x_2=-2, y_2=2$ replacing in the formula:

$m=\frac{2-4}{(-2)-(-6)} \\\\m=\frac{-2}{4} \\\\m=-\frac{1}{2}$

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

We have to find b, we can find it replacing either of the points in $y=-\frac{1}{2}x+b$

Replacing with (-2,2),

$y=-\frac{1}{2}x+b\\2=-\frac{1}{2}.(-2)+b\\2=1+b\\2-1=b\\1=b$

or replacing with (-6,4)

$y=-\frac{1}{2}x+b\\4=-\frac{1}{2}.(-6)+b\\4=3+b\\4-3=b\\1=b$

You can see that the result is the same, then the equation of the line is:

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