Find the slope-intercept equation of the line perpendicular to the line x - 3y = 4 and containing the point (6,-9).
First, let's rewrite the equation in standard slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept:
x-3y = 4
-3y = 4 - x (Subtract x from both sides)
y = (1/3)x -4 (Divide both sides by -3)
The slope of this line is m = 1/3. If the slope of a line is m, the slope of the line perpendicular to it is -1/m. So the slope of a line that's perpendicular to y = (1/3)x - 4 is mp = -1/(1/3) = -3.
OK, we're half way there. We want to find the formula of line perpendicular to y = (1/3)x - 4. We know it will have a slope mp = -3 and the line passes through the point (6,-9)
y = (-3)x + b
-9 = (-3)(6) + b (Plug in -9 for y, 6 for x)
-9 = -18 + b
9 = b (Solve for b)
So our equation is:
y = -3x + 9