Answer:
Explanation:
To find the distance from the origin to the graph of 3x - y + 1 = 0, we need to find the perpendicular distance from the origin to the line.
First, let's rearrange the equation into slope-intercept form, which is y = mx + b, where m is the slope of the line and b is the y-intercept:
3x - y + 1 = 0
y = 3x + 1
So, the slope of the line is m = 3.
The perpendicular distance from the origin to the line is given by the formula:
distance = |(Ax0 + By0 + C)/sqrt(A^2 + B^2)|
where (x0, y0) is a point on the line, A, B, and C are the coefficients of the equation of the line. In this case, (x0, y0) can be taken as (0, 0), since we want to find the distance from the origin.
So, we have:
distance = |(30 - 10 + 1)/sqrt(3^2 + (-1)^2)|
distance = |1/sqrt(10)|
distance = sqrt(1/10)
Therefore, the distance from the origin to the graph of 3x - y + 1 = 0 is sqrt(1/10), which is option c.