The line below that is represented by the equation, y=2/5X+1/2. Which of the following is the equation for a line is perpendicular to this line passing through the point (2,2)?
The format of the equation of a line is y = mx + b, where m = the line's slope and b = the line's y-intercept (where it crosses the y-axis). In the equation given, m = 2/5.
When lines are perpendicular, their slopes are negative reciprocals of each other. Remember that to take a reciprocal of a fraction, you flip it upside down... in this case, the slope of the perpendicular line will be -5/2 (flip it and change the sign).
At this point, plug what you know into the formula for the second line: y = mx + b becomes
y = -5/2 x + b
It may seem like you don't have enough information at this point to solve the problem - you know m, but you still need to find b. Go back and read the question again - it tells you the perpendicular line goes through the point (2,2). Remember that is in the form (x,y). You can plug the value for x and the value for y given to you by the point into the formula...
(2) = -5/2 (2) + b
Now you just need to solve for b. Once you have a value for b, plug it into the formula (y = -5/2 x + b) and you'll be finished.
Good luck! Most students, once they learn the rule about the slope being the negative reciprocal, get hung up because they forget to plug the x and y values from the point into the formula to calculate b in these types of questions. If you are given a point, you always have numbers you can plug in for x and y.