What is the equation of a line with a slope of 2 that passes through the origin?

To find the equation of a line, we can use the slope-intercept form, which is given by the equation ( y = mx + b ), where ( m ) represents the slope and ( b ) represents the y-intercept. In this case, we know that the slope ( m ) is 2, and since the line passes through the origin, the y-intercept ( b ) is 0.

Substituting these values into the slope-intercept form gives us:

[

y = 2x + 0

]

This simplifies to:

[

y = 2x

]

Thus, the equation of the line with a slope of 2 that passes through the origin is represented as ( y = 2x ). This means for every unit increase in ( x ), ( y ) will increase by 2 units, consistent with the given slope.