To find the distance from a point to a line we can use the formula for the distance between a point and a line. The formula is:
Distance = |Ax + By + C| / sqrt(A^2 + B^2)
Where (x y) is the point and A B and C are the coefficients of the line equation in the form Ax + By + C = 0.
Given the line equation y = -2x + 8 we can rewrite it in the form Ax + By + C = 0 by adding 2x to both sides:
2x + y - 8 = 0
Now we can compare the coefficients:
A = 2
B = 1
C = -8
The point Q(6 1) has coordinates (x y) = (6 1).
Plugging these values into the distance formula we get:
Distance = |(2 * 6) + (1 * 1) - 8| / sqrt(2^2 + 1^2)
= |12 + 1 - 8| / sqrt(4 + 1)
= |5| / sqrt(5)
= 5 / sqrt(5)
= sqrt(5)
Therefore the distance from the point Q(6 1) to the line y = -2x + 8 is sqrt(5) (approximately 2.236).