Final answer:
To find the distance between a point (3, 5) and a line with the equation 5x – 3y + 10 = 0, we can use the formula for the distance from a point to a line.
Step-by-step explanation:
To find the distance between a point and a line, we can use the formula for the distance from a point to a line. The equation of the given line is 5x – 3y + 10 = 0. We can rewrite this equation in slope-intercept form as y = (5/3)x - 10/3. The formula to find the distance between a point (x1, y1) and a line y = mx + b is given by: distance = |y1 - mx1 - b| / sqrt(1 + m^2). Plugging in the values for the point (3, 5) and the line equation, the distance can be calculated as |5 - (5/3) * 3 - (-10/3)| / sqrt(1 + (5/3)^2). This simplifies to |5 - 5 + 10/3| / sqrt(1 + 25/9) = |10/3| / sqrt(34/9). Finally, this can be further simplified to 10 / 3 * sqrt(9/34) = 10 * sqrt(9) / 3 * sqrt(34) = 30 / sqrt(34) units.