SOLUTION: Find the slope-intercept form of the equation of the line that passes through (2, −1) and is perpendicular to 8x + 3y = 9.

Algebra ->  Linear-equations -> SOLUTION: Find the slope-intercept form of the equation of the line that passes through (2, −1) and is perpendicular to 8x + 3y = 9.      Log On


   

Question 1196328: Find the slope-intercept form of the equation of the line that
passes through (2, −1) and is perpendicular to 8x + 3y = 9.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
the slope-intercept form of the equation of the line;
y-y%5B1%5D=m%28x-x%5B1%5D%29
passes through (2, -1)
perpendicular to 8x+%2B+3y+=+9

first find the slope of given line
8x+%2B+3y+=+9
++3y+=+-8x%2B9
++y+=+-%288%2F3%29x%2B9%2F3
++y+=+-%288%2F3%29x%2B3
so, a slope is m=-%288%2F3%29

recall that perpendicular lines have slopes negative reciprocal to each other, so the slope of the line perpendicular to given line will be
m=-1%2F%28-8%2F3%29
m=3%2F8

now use given point and a slope to find equation
y-y%5B1%5D=m%28x-x%5B1%5D%29..........plug in the coordinates of the point (2, -1) and the slope m=3%2F8

y-%28-1%29=%283%2F8%29%28x-2%29
y%2B1=%283%2F8%29%28x-2%29
y%2B1=%283%2F8%29x-%283%2F8%292
y%2B1=%283%2F8%29x-3%2F4
y=%283%2F8%29x-3%2F4-1
y=%283%2F8%29x-7%2F4=> your line