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 (
Solución de tutoría real
Responder
Solución
Revisado y aprobado por el equipo de tutoría de UpStudy
Beyond the Answer
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!