M:N:MC:1

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

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

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$minus 2 over 5$

Correct Answer:

$minus 3 over 2$

Correct Answer:

Yes

$minus 8 over 9$

Correct Answer:

$minus 11 over 14$

Correct Answer:

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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:

easy

Objective:

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

Math

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M:N:MC:1

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