What is the equation of a line that passes through the origin and the point (1, 2)?

To find the equation of a line that passes through the origin (0, 0) and a given point, in this case, (1, 2), we can use the slope-intercept form of a line, which is:

y = mx + b

Here, m represents the slope and b is the y-intercept. Since the line passes through the origin, we know that b = 0. Therefore, the equation simplifies to:

y = mx

Next, we need to determine the slope m. The slope can be found using the formula:

m = (y₂ – y₁) / (x₂ – x₁)

In our case, we have two points: the origin (0, 0) and the point (1, 2). Substituting these points into the slope formula gives:

m = (2 – 0) / (1 – 0) = 2/1 = 2

Now that we have identified the slope as 2, we can substitute this value back into our equation:

y = 2x

So, the final equation of the line that passes through the origin and the point (1, 2) is:

y = 2x

This equation indicates that for every unit increase in x, y increases by 2 units, demonstrating a positive linear relationship between x and y.