Final answer:
To find the equation of a line that is perpendicular to 2y = 3x - 10 and passes through (6, m), we need to determine the slope of the given line. The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line. Using the point-slope form of an equation, we can find the equation of the line perpendicular to the given line and passing through (6, m).
Step-by-step explanation:
To find an equation of a line that is perpendicular to the line whose equation is 2y = 3x - 10 and passes through (6, m), we need to determine the slope of the given line. The slope of a line can be determined by dividing the change in the y-values by the change in the x-values. In this case, the slope is 3/2. The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line. Therefore, the slope of the perpendicular line is -2/3.
Now that we have the slope of the perpendicular line, we can use the point-slope form of an equation to find the equation of the line. The point-slope form is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Plugging in the values (6, m) and -2/3 for the slope, we get the equation y - m = -2/3(x - 6). Simplifying this equation gives us the equation of the line perpendicular to 2y = 3x - 10 and passing through (6, m).