Final answer:
The equation of a line with a slope of 1/2 that passes through the origin is y = (1/2)x. This equation is both the point-slope form and the slope-intercept form since the y-intercept is 0.
Step-by-step explanation:
The student is asking for the equation of a linear equation with a slope of 1/2 that passes through the origin. The point-slope form of the line's equation is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Since the line passes through the origin, which is the point (0, 0), we can substitute these values into the point-slope form equation. Therefore, the equation becomes y - 0 = (1/2)(x - 0), or simply y = (1/2)x.
In slope-intercept form, which is expressed as y = mx + b, where m is the slope and b is the y-intercept, the equation of the line is simply y = (1/2)x since the line passes through the origin and the y-intercept is 0.