Final answer:
To find the equation of a line through the origin and (10, 2) in standard form, first calculate the slope (1/5), then write the equation y = (1/5)x, and convert it to standard form, resulting in 10x - 2y = 0.
Step-by-step explanation:
The question involves finding an equation of a line that passes through the origin (0,0) and a specific point (10, 2). To write the equation of this line in standard form, we first find the slope of the line that passes through these two points. The slope is determined by the formula (change in y)/(change in x), which in this case gives us (2 - 0)/(10 - 0) = 2/10 = 1/5.
Once we have the slope, we can use the point-slope form of a line, which is y - y1 = m(x - x1). Because our line passes through the origin, we have x1 = 0 and y1 = 0, so our equation simplifies to y = (1/5)x. To convert this to standard form, we clear the fraction by multiplying everything by 5 to get 5y = x. Finally, we move all terms to one side to get x - 5y = 0, which is the standard form.
The correct choice is the one which mirrors this equation: Option B): 10x - 2y = 0 is the correct standard form equation for the line passing through the origin and (10, 2).