A graph titled Monthly Sales and Advertising Costs has Advertising Costs (1,000 dollars) on the x-axis and sales (1,000 dollars) on the y-axis. A line goes through points (6.4, 117) and (6.6, 120).

Question

A graph titled Monthly Sales and Advertising Costs has Advertising Costs (1,000 dollars) on the x-axis and sales (1,000 dollars) on the y-axis. A line goes through points (6.4, 117) and (6.6, 120).
The scatterplot and trend line show a positive correlation between advertising costs and sales.

The slope was found using the points (6.4, 117) and (6.6, 120). What is the value of b in the equation of the trend line?

y = 15x + b

GPT-4o mini · Answer

To find the value of $ b $ in the equation of the trend line $ y = 15x + b $, we first need to use one of the given points to solve for $ b $. We have two points: - $ (6.4, 117) $ - $ (6.6, 120) $ Given that the slope $ m $ of the line is $ 15 $, we can substitute one of the points into the equation to find $ b $. Let's use the point $ (6.4, 117) $. Substituting these values into the equation gives us: $$ 117 = 15(6.4) + b $$ Calculating $ 15(6.4) $: $$ 15 \times 6.4 = 96 $$ Now we can substitute this back into the equation: $$ 117 = 96 + b $$ To solve for $ b $, subtract $ 96 $ from both sides: $$ b = 117 - 96 = 21 $$ Thus, the value of $ b $ in the equation of the trend line is $ \boxed{21} $.