Final answer:
To find the equation of the line perpendicular to 9x + 12y = 15 that passes through (10, 16), we first find the slope of the original line. The perpendicular slope is the negative reciprocal of the original slope, which turns out to be ⅓. Using this slope and the given point, we derive the slope-intercept form of the new line: y = ⅓x + ⅓³.
Step-by-step explanation:
To write an equation for a line that is perpendicular to the graph of 9x + 12y = 15 and passes through the point (10, 16), we first need to find the slope of the original line. By rearranging the original equation into slope-intercept form (y = mx + b), where m represents the slope, we get y = -¾ x + ⅛. Therefore, the slope of the original line is -¾.
Since perpendicular lines have slopes that are negative reciprocals of each other, the slope of the line we want to find will be the negative reciprocal of -¾, which is ⅓. Using the point-slope form of the equation y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope, we get y - 16 = ⅓(x - 10).
To write this in slope-intercept form (y = mx + b), we solve for y:
y = ⅓x - ⅓(10) + 16 = ⅓x - ⅓ + 16
After simplifying, we have the final equation:
y = ⅓x + ⅓³