Question

what is the equation of the line in slope intercept form that passes through the point 3 -5 and is perpendicular to the line y = 3x - 6

Answer 1

Perpendicular means its slope is the negative reciprocal of the other line. The other line's slope is 3, so the slope of the line you're trying to find is -1/3. Now that you know the slope and have a coordinate it passes through, you can generate its equation by plugging those values into the slope-intercept form and solving for b:\[y=mx+b\]\[-5=-\left(\frac{1}{3}\right)(3)+b\]\[-4 = b\]Now that you have b, you have your full equation:\[y=-\left(\frac{1}{3}\right)x-4\]