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Heart of Algebra


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Line straight ell is graphed in the xy-plane below.

The figure presents a xy-coordinate plane with the graph of a line and 2 points. There are equally-spaced tick marks on both axes. The fifth tick mark on the x¬-axis to the right of the origin and the fifth tick mark above the origin are labeled 5. The fifth tick mark to the left of the origin and the fifth tick mark below the origin are labeled negative 5. The line slants down and to the right, intersecting the y-axis at the seventh tick mark above the origin and intersecting the x-axis between the fourth and fifth tick marks to the right of the origin. The 2 points appear equally spaced on the line shown.

If line straight ell is translated up 5 units and right 7 units, then what is the slope of the new line?

Select an Answer

minus 2 over 5

Correct Answer: 

minus 3 over 2

Correct Answer: 

minus 8 over 9

Correct Answer: 

minus 11 over 14

Correct Answer: 

Choice B is correct. The slope of a line can be determined by finding the difference in the y-coordinates divided by the difference in the x-coordinates for any two points on the line. Using the points indicated, the slope is minus 3 over 2. Translating the line moves all the points on the line the same distance in the same direction, and the image will be a parallel line. Therefore, the slope of the image is minus 3 over 2.

Choice A is not the correct answer. This value may result from a combination of errors. The student may misunderstand how the negative sign affects the fraction and apply the transformation as fraction numerator left parenthesis minus 3 plus 5 right parenthesis over denominator left parenthesis minus 2 plus 7 right parenthesis end fraction.

Choice C is not the correct answer. This value may result from finding the slope of the line and then subtracting 5 from the numerator and 7 from the denominator.

Choice D is not the correct answer. This answer may result from adding 5 over 7 to the slope of the line.

Question Difficulty: 

Students must make a connection between the graphical form of a relationship and a numerical description of a key feature.