Final answer:
To calculate the distance from the point (-1, 4) to the line with slope -3 passing through (2, -4), find the equation of the line, then use the distance formula. The calculated distance, when rounded, is approximately 1.6 units.
Step-by-step explanation:
To find the distance from the point (-1, 4) to the line with a slope of -3 that passes through the point (2,-4), we can use the point-slope form to find the equation of the line and then use the distance formula for a point to a line.
The equation of the line can be written in point-slope form as:
y - (-4) = -3(x - 2), which simplifies to y + 4 = -3x + 6, and further simplifies to y = -3x + 2.
The distance d from a point (x0, y0) to a line given by ax + by + c = 0 is given by the formula:
d = |ax0 + by0 + c| / √(a^2 + b^2)
For the line y = -3x + 2, we have a = -3, b = 1, and c = -2. Plugging in the points (-1, 4) into the distance formula gives us:
d = |-3(-1) + 1(4) - 2| / √((-3)^2 + 1^2) = |3 + 4 - 2| / √(9 + 1) = |5| / √10 = 5 / √10. When rounded to the nearest tenth, the distance is approximately 1.6 units.