Question #002dba45 - SAT Suite Question Bank

ID: 002dba45

Modded SAT Question Bank by Abdullah Mallik

Line $k$ is defined by $y = - \frac{17}{3} x + 5$ . Line $j$ is perpendicular to line $k$ in the xy-plane. What is the slope of line $j$ ?

Toggle Answer

Tip: Press CTRL/Command to toggle answer

Correct Answer: .1764, .1765, 3/17

Rationale

The correct answer is $\frac{3}{17}$ . It’s given that line $j$ is perpendicular to line $k$ in the xy-plane. This means that the slope of line $j$ is the negative reciprocal of the slope of line $k$ . The equation of line $k$ , $y = - \frac{17}{3} x + 5$ , is written in slope-intercept form $y = m x + b$ , where $m$ is the slope of the line and $b$ is the y-coordinate of the y-intercept of the line. It follows that the slope of line $k$ is $- \frac{17}{3}$ . The negative reciprocal of a number is $negative 1$ divided by the number. Therefore, the negative reciprocal of $- \frac{17}{3}$ is $\frac{- 1}{- \frac{17}{3}}$ , or $\frac{3}{17}$ . Thus, the slope of line $j$ is $\frac{3}{17}$ . Note that 3/17, .1764, .1765, and 0.176 are examples of ways to enter a correct answer.

Question Difficulty: Medium