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Jasmine plays a game on her phone. The scatter plot shows her score and the number of minutes she ploys. A good line of fit is drown through the points \( (10,55) \) and (16, 82). \( m= \) 4.5 What is the \( y \)-intercept of the line of fit? \[ b= \] \( \square \) 7 18 9 (

Ask by Munoz Coleman. in the United States
Jan 23,2025

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The \( y \)-intercept \( b \) of the line of fit is 10.

Solución

To find the \( y \)-intercept \( b \) of the line of fit, we can use the slope-intercept form of a linear equation, which is given by: \[ y = mx + b \] where: - \( m \) is the slope, - \( b \) is the \( y \)-intercept, - \( x \) is the independent variable (in this case, the number of minutes played), - \( y \) is the dependent variable (the score). ### Step 1: Use the slope \( m \) We are given that the slope \( m = 4.5 \). ### Step 2: Use one of the points to find \( b \) We can use one of the points on the line to find \( b \). Let's use the point \( (10, 55) \). Substituting \( x = 10 \), \( y = 55 \), and \( m = 4.5 \) into the equation: \[ 55 = 4.5(10) + b \] ### Step 3: Solve for \( b \) Calculating \( 4.5(10) \): \[ 4.5(10) = 45 \] Now substituting back into the equation: \[ 55 = 45 + b \] To isolate \( b \), we subtract 45 from both sides: \[ b = 55 - 45 \] \[ b = 10 \] ### Conclusion The \( y \)-intercept \( b \) of the line of fit is: \[ b = 10 \] Thus, the answer is: \[ b = 10 \]

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To find the \( y \)-intercept \( b \) of the line of fit, we start with the slope-intercept form of a linear equation: \( y = mx + b \). We have the slope \( m = 4.5 \) and can use one of the points, say \( (10, 55) \), to solve for \( b \). Plugging in the point: \[ 55 = 4.5(10) + b \] Calculating \( 4.5 \times 10 = 45 \): \[ 55 = 45 + b \] Now, isolating \( b \): \[ b = 55 - 45 = 10 \] So, the \( y \)-intercept \( b \) is \( 10 \). --- While graphs and lines can seem tedious, they play a vital role in data analysis, helping to visualize relationships. Scatter plots and line of best fit can reveal patterns—like Jasmine's score improvements over time—that might otherwise go unnoticed! Additionally, if you're getting familiar with slope and intercepts, getting hands-on with graphing software or plotting points manually can process the math visually! It's a fun way to see your equations come to life, like turning abstract numbers into a colorful map of scores and time!

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