Question

a person pays an $8 cover charge to hear a hip - hop band. let t be the total cost (in dollars) of the cover charge plus d dollars spent on drinks. complete parts (a) through (e).
b. perform a unit analysis of the equation found in the previous step.
the units of the expressions on both sides of the equation are dollars.
c. graph the equation. choose the correct answer.
\\(\bigcirc\\) a.
\\(\bigcirc\\) b.
\\(\bigcirc\\) c.
\\(\bigcirc\\) d.

Explanation:

Step1: Determine the equation

First, the total cost \( T \) is the cover charge (\$8) plus the cost of drinks (\( d \) dollars). So the equation is \( T = d + 8 \). This is a linear equation in the form \( y = mx + b \), where the slope \( m = 1 \) (positive, so the line should have a positive slope) and the y - intercept \( b = 8 \) (when \( d = 0 \), \( T = 8 \)).

Step2: Analyze the graphs

• Graph A: Let's check the slope and intercept. If the slope is close to 0 (almost horizontal), it doesn't match \( T=d + 8 \) (slope 1).
• Graph B: The line has a negative slope, but our equation has a positive slope (\( T \) increases as \( d \) increases), so B is incorrect.
• Graph C: The y - intercept seems to be less than 8 (maybe 0 or a small number), which doesn't match \( T=d + 8 \) (when \( d = 0 \), \( T = 8 \)).
• Graph D: The line has a positive slope (since as \( d \) increases, \( T \) increases) and when \( d = 0 \), \( T=8 \) (matches the y - intercept of our equation \( T=d + 8 \)). Also, the slope is 1 (for every 1 unit increase in \( d \), \( T \) increases by 1 unit), which is consistent with the equation.

Answer:

D (the graph labeled D, which has a positive slope, y - intercept at \( T = 8 \) when \( d = 0 \), and shows \( T \) increasing as \( d \) increases)