Find the equation of the line below. Arrange your answer in the form y = mx + b, where b is the constant.

The coordinates are (-2,2) and (2,-2)

Question

Find the equation of the line below. Arrange your answer in the form y = mx + b, where b is the constant.

The coordinates are (-2,2) and (2,-2)

igreen · Answer

You can find the slope first.

Slope of a line: $m = \dfrac{y_2-y_1}{x_2-x_1}$

In this case:

$y_2 = -2$
$y_1 = 2$

$x_2 = 2$
$x_1 = -2$

Plug them in:

$m = \dfrac{-2-2}{~~~2+2}$

Add & Subtract:

$m = \dfrac{-4}{~~~4}$

Can you divide that? @madison.bush

anonymous · Answer

m=-1 @iGreen

igreen · Answer

Yep, so the slope is -1.

In y = mx + b

m is the slope, so we can put -1 in:

y = -x + b

Also, if you draw a line through (-2, 2) and (2, -2), you'll see that they cross through the x and y-axes at (0, 0), which means the y-intercept is 0.

So our final equation is:

y = -x + 0

or

y = -x

igreen · Answer

Understand? @madison.bush

anonymous · Answer

yeah. thanks. but my assignment marked it wrong. thats what i put a little while ago and when it was graded it was wrong. @iGreen

nincompoop · Answer

OR without the aid of a graph and just by pure analysis:
after obtaining the slope, $m = -1$, use the slope intercept form $y-y_1 = m(x-x_1) $ to solve for y

$y-2 = -1(x-(-2)) \rightarrow  y-2 = -x+2 \rightarrow \huge y=-x $