To determine the shortest distance from the point (-2, 5) to the line y = (3/4)x + 3, we can use the formula for the distance between a point and a line.
The formula for the distance between a point (x₁, y₁) and a line Ax + By + C = 0 is given by:
Distance = |Ax₁ + By₁ + C| / sqrt(A² + B²)
In this case, the equation of the line is y = (3/4)x + 3, which can be rearranged to the form -3/4x + y - 3 = 0. Comparing this equation to the general form Ax + By + C = 0, we can see that A = -3/4, B = 1, and C = -3.
Now, substituting the values into the formula:
Distance = |-3/4 * (-2) + 1 * 5 - 3| / sqrt((-3/4)² + 1²)
Simplifying:
Distance = |6/4 + 5 - 3| / sqrt(9/16 + 1)
Distance = |15/4 - 3| / sqrt(9/16 + 16/16)
Distance = |15/4 - 12/4| / sqrt(25/16)
Distance = |3/4| / sqrt(25/16)
Distance = 3/4 / 5/4
Distance = 3/4 * 4/5
Distance = 3/5
Therefore, the shortest distance from the point (-2, 5) to the line y = (3/4)x + 3 is 3/5 units.