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Calculating the Slope of a Line

Link of the Day

On this day in 1968, James Earl Ray, an escaped American convict, was arrested and charged with the assassination of Dr. Martin Luther King. Ray was in the process of trying to escape Rhodesia when he was apprehended. He was eventually convicted and sentenced to 99 years in prison. You can read more about James Earl Ray here.


6/8 Calculating the slope of a Line

Read the following SAT test question and then click on a button to select your answer. 


In the xy-plane, line l passes through the points 0 comma 0and 2 comma 5. Line m is perpendicular to line l. What is the slope of line m?


The first step here is to identify the bottom line. In this case we are looking for the slope of a line that is perpendicular to the line that passes through the points (0,0) and (2,5). The first step to answering this problem is to calculate the slope of the line that passes through the points given. Remember that the slope of a line is equal to the rise over the run so you have 


It is essential that you don't forget to answer the bottom line for this question. Although this is a fairly easy question, it is very easy to make a sloppy mistake and miss some easy points. We are looking for the slope of a line that is perpendicular to the line that passes through the points given. The slope of a  perpendicular line is always the negative reciprocal of the slope of the line it is perpendicular to. So we take the original slope we calculated, negate it, and flip it.



Now we simply look at the answers and choose the answer that matches our prediction.

(A) negative 5 over 2
(B) negative 2 over 5
(C) 2 over 5
(D) 5 over 2
(E) 5

As you can see, answer B matches our prediction exactly. Note that if we had failed to answer the bottom line and only calculated the slope of the line that went through the points, we would have picked answer (D). Even though this was a fairly easy problem, more than 50% of the responses were incorrect!

On sat.collegeboard.com 49% of the responses were correct.

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