Final answer:
To find the distance from a point to a line, use the formula for the distance between a point and a line in coordinate geometry.
Step-by-step explanation:
To find the distance from a point to a line, we can use the formula for the distance between a point and a line in coordinate geometry. The formula is given by:
distance = |Ax + By + C| / sqrt(A^2 + B^2)
In this case, the line equation is X + 5y = 10. We can rewrite this equation as 5y = -X + 10 and then divide every term by 5 to get y = (-1/5)X + 2.
Using the given point (0, -4) and substituting the values of A, B, and C into the formula, we have:
distance = |0(-1) + (-4)(5) - 10| / sqrt((-1)^2 + (-4)^2)
distance = |-20 - 10| / sqrt(1 + 16)
distance = |-30| / sqrt(17)
distance ≈ 2.343 units (rounded to the nearest tenth of a unit).