Question

the number of hate crime convictions in a particular region was 26 convictions in 2006 and has declined by about 4 convictions each year since then. let n be the number of hate crime convictions in the year that is t years since 2006. complete parts (a) through (e). c. in the equation, the units on both sides are years, so the equation is correct. (c) graph the equation by hand found in part (a). choose the correct graph. a. b. c. d.

Explanation:

Step1: Determine the equation

From part (a), the linear equation should be \( n = 26 - 4t \) (since it starts at 26 in 2006 (\( t = 0 \)) and decreases by 4 each year).

Step2: Analyze the graph features

• When \( t = 0 \), \( n = 26 \), so the y - intercept (n - intercept here) should be around 26.
• The slope is - 4, so the line should be decreasing (going down from left to right).

Step3: Compare with the graphs

• Graph A: At \( t = 0 \), \( n\approx28 \) (close to 26), and it is a decreasing line.
• Graph B: Starts at \( n = 0 \) when \( t = 0 \), increasing, so incorrect.
• Graph C: At \( t = 0 \), \( n\approx24 \) (not 26), so incorrect.
• Graph D: Starts at \( n = 0 \), increasing, incorrect.

Answer:

A. The graph with n - intercept around 28 (close to 26) and a decreasing line from (0, ~28) to (8, 0)