Question

Line is graphed in the $xy$-plane below.If line is translated up $5$ units and right $7$ units, then what is the slope of the new line?

• A. $\frac{-2}{5}$
• B. $\frac{-3}{2}$
• C. $\frac{-8}{9}$
• D. $\frac{-11}{14}$

Answer 1

The correct option is B $\frac{-3}{2}$

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.