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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)?

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MaryJane S. | National standardized test prep and college teaching experienceNational standardized test prep and coll...

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.