Final answer:
To find the point on the line -5x + 4y + 2 = 0 that is closest to the point (3,2), we need to find the point on the given line that has the shortest distance to the point (3,2). By using the distance formula and minimizing the distance, we can find the desired point.
Step-by-step explanation:
To find the point on the line -5x + 4y + 2 = 0 that is closest to the point (3,2), we need to find the point on the given line that has the shortest distance to the point (3,2).
First, let's rewrite the equation of the line in slope-intercept form: 4y = 5x - 2 => y = (5/4)x - 1/2.
Next, we can use the distance formula to calculate the distance between each point on the line and the point (3,2). The distance formula is: d = sqrt((x2-x1)^2 + (y2-y1)^2).
By substituting the coordinates of the point (3,2) and the equation of the line into the distance formula, we can find the point on the line that is closest to (3,2) by minimizing the distance.