Question

1. which of the following could be the equation for the line of best fit? scatter plot with a line of best fit options: ( y = -4x + 18 ), ( y = 4x - 18 ), ( y = -18 - 4x ), ( y = 4x + 18 )

Explanation:

Step1: Analyze the slope

The line of best fit in the graph is increasing, so the slope should be positive. Let's check the slopes of each option:

• For \( y = -4x + 18 \), slope \( m=-4 \) (negative, eliminate).
• For \( y = 4x - 18 \), slope \( m = 4 \) (positive), but let's check the y - intercept.
• For \( y=-18 - 4x \), slope \( m=-4 \) (negative, eliminate).
• For \( y = 4x+18 \), slope \( m = 4 \) (positive).

Step2: Analyze the y - intercept

From the graph, when \( x = 0 \), the line of best fit intersects the y - axis at a positive value. Let's check the y - intercepts:

• For \( y = 4x - 18 \), when \( x = 0 \), \( y=-18 \) (negative, not matching the graph).
• For \( y = 4x + 18 \), when \( x = 0 \), \( y = 18 \) (positive, matches the graph's y - intercept behavior as the line starts at a positive y - value when \( x = 0 \)).

Answer:

\( y = 4x + 18 \)