What is the equation of the line?

Question

asked Jul 23, 2020 95.7k views

1 Answer

Mark Sonn · Answer 1 · 2020-07-28T06:08:07+0000

A line has an equation of a form,

y=ax+b

From a graph we can pick two points on the line, say A and B where,

$A(x_1,y_2),B(x_2,y_2)\longrightarrow A(0,0),B(1,-1)$

Using their coordinates we are able to calculate slope.

$a=\frac{\Delta{y}}{\Delta{x}}=(y_2-y_1)/(x_2-x_1)=(-1-0)/(1-0)=-1$

Hence,

$y=-1\cdot x+b$

The x and y terms can be replaced with coordinates of one point either A or B. I'll pick A.

$0=-1\cdot0+b$

And now solve for b.

$0=0+b\Longrightarrow b=0$

Hence,

$y=-1\cdot x+0$

Simply,

$\boxed{y=-x}$

Hope this helps.

r3t40