Question

What is the equation of a line passing through the origin with a slope of positive one?

Answer 1

y=x
The slope of this line is 1 (the numerical coefficient of x) and passes through the origin (if you put x=0 it gives you y=0).

Answer 2

We are going to use the equation of a line y = mx + b. In this equation, m is the slope and b is the y-intercept.

We know from the question that the slope is 1. Therefore, m = 1. So now, our line is y = 1x + b

Then, we can use a known point on the line to find b. We know that our line passes through the origin so point (0,0) is on the line.
0 = 1(0) + b
0 = 0 + b
b = 0

Therefore, the equation of the line is:
y = 1x + 0
or just y = x