Question

1. which of the following could be the equation for the line of best fit? graph of a scatter plot with a line of best fit options: ( y = -23 - 5x ), ( y = -5x + 23 ), ( y = 5x - 23 ), ( y = 5x + 23 )

Explanation:

Step1: Analyze the slope

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

• \( y = -23 - 5x \): slope \( m = -5 \) (negative, eliminate)
• \( y = -5x + 23 \): slope \( m = -5 \) (negative, eliminate)
• \( y = 5x - 23 \): slope \( m = 5 \) (positive)
• \( y = 5x + 23 \): slope \( m = 5 \) (positive)

Step2: Analyze the y-intercept

The y-intercept (b) is where the line crosses the y-axis. From the graph, the line crosses the y-axis below the origin (negative y-intercept).

• \( y = 5x - 23 \): y-intercept \( b = -23 \) (negative)
• \( y = 5x + 23 \): y-intercept \( b = 23 \) (positive, eliminate)

Answer:

\( y = 5x - 23 \)