Question

Write the equation of a line that is perpendicular to y=7/5x+6 and that passes through the point (2,-6)

Answer 1

First look at the slope. A perpendicular line will have a negative reciprocal slope of the given line.
y = -5/7x + ?
Now to find the y-intercept, substitute the given points (2, -6) into the equation and solve for b.
y = mx + b
-6 = -5/7(2) + b
-6 = -10/7 + b
Now get rid of -10/7 by using the subtraction property of equality (so add 10/7 to -10/7 to cancel it out and to -6)
-32/7 = b

The correct answer would be y = -5/7x - 32/7 (or y = -5/7x - 4.57 depending on which format it's wanted in)