Final answer:
The equation of the line that is perpendicular to the line y = -6/5x + 2 and passes through the point (6,3) can be found by using the negative reciprocal of the original slope (5/6) and applying the point-slope form, resulting in the equation y = 5/6x - 2.
Step-by-step explanation:
The question asks for the equation of a line that is perpendicular to the line with the equation y = -6/5x + 2 (ignoring the typo). To find this equation, we first need to determine the slope of the perpendicular line. Since the slope of the given line is -6/5, the slope of the line perpendicular to it will be the negative reciprocal of that, which is 5/6. Next, we use the point (6, 3) that the new line passes through, along with the slope of 5/6, to write the equation in the point-slope form, which is y - y1 = m(x - x1).
Substituting the values, we get:
y - 3 = 5/6 * (x - 6)
This can be simplified and written in the slope-intercept form, y = mx + b, by distributing the slope and then solving for y:
y = 5/6x - 5 + 3
Simplifying further, we get the final equation: y = 5/6x - 2.