Also tell the functional relationship y= **Problem Statement:**When \(\log y\) is graphed as a function of \(x\), a straight line results. Graph a straight line, given by two points, on a log-linear plot, and determine the functional relationship. (The original x-y coordinates are given).Points:- \((x_1, y_1) = (-1, 1)\)- \((x_2, y_2) = (1, 5)\)**Task:**Graph a straight line on a log-linear plot.**Graph Options:**1. **Graph A:** - X-axis: Ranges from -4 to 10. - Y-axis: Shows values as 1, 2, 4, 6, 8, 10. - The line is increasing steadily from near the bottom left towards the top right, indicating a positive slope.2. **Graph B:** - X-axis: Ranges from -4 to 10. - Y-axis: Displays logarithmic values (base 10): \(10^0, 10^2, 10^4, 10^6, 10^8, 10^{10}\). - The line is increasing steadily, forming a straight positive slope on the logarithmic scale.3. **Graph C:** - X-axis: Ranges from -4 to 10. - Y-axis: Displays logarithmic values (base 10): \(10^0, 10^2, 10^4, 10^6, 10^8, 10^{10}\). - The line is decreasing from top left to bottom right, indicating a negative slope.4. **Graph D:** - X-axis: Ranges from -4 to 10. - Y-axis: Shows values as 1, 2, 4, 6, 8, 10. - The line is decreasing, moving from the top left to the bottom right, indicating a negative slope.The goal is to determine which graph represents the functional relationship between \(x\) and \(\log y\) such that the plotted data points form a straight line indicating the correct linear relationship in a log-linear context.

Name: Also tell the functional relationship y= **Problem Statement:**When \(
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: Also tell the functional relationship y= **Problem Statement:**When \(\log y\) is graphed as a function of \(x\), a straight line results. Graph a straight line, given by two points, on a log-linear plot, and determine the functional relationship. (T

Two points x1,y1=-1,1 and x2,y2=1,5. We have graph a straight line given by these two points on a log-linear plot and determine the functional relationship.The slope of the line in the log-linear plane is logy2-logy1x2-x1. The equation of the line in the log-linear plane logy-logy1=logy2-logy1x2-x1x-x1 Use the above formula to find the slope of the line passing through x1,y1=-1,1 and x2,y2=1,5. m=logy2-logy1x2-x1=log5-log11-(-1)=log5-01+1=12log5=log512 Hence the line of the equation passing through the point (-1,1) is logy-logy1=mx-x1logy-log1=log512x+1logy=log512x+1logy=xlog512+log512logy=log5x2+log512logy=log55xy=55x Hence the functional relationship is y=55x. To plot points on the log-linear graph the y-axis takes the values logy. Hence when x=1, log1=0, and x=5, log5=0.69 Hence option (b) is true.