yoylenbarrosousa
Answered

hello please help me on both parts A and B. ♡♡
i attached a photo of the answer choices and the question asked in part B + the graph
please explain your answers !


The fuel economy of a car is its average distance traveled per amount of fuel consumed. Cars have different fuel economies when they are driven in the city and on the highway. A linear model of the relationship between the city and highway fuel economies of eight cars, in miles per gallon (mpg), is shown.

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hello please help me on both parts A and B i attached a photo of the answer choices and the question asked in part B the graphplease explain your answers The fu class=


Answer :

sqdancefan

Answer:

  Part A: (a) y = 2/3x +19

  Part B: 47.67 mpg

Step-by-step explanation:

You want an approximate line of best fit for the data in the scatterplot, and the y-value it gives for an x-value of 43.

A. Line

The line of best fit will go near the points at lower left and upper right. Those points are (32, 40) and (40, 46). The slope of the line will be given by ...

  m = (y2 -y1)/(x2 -x1)

  m = (46 -40)/(40-32) = 6/8 = 3/4

This value of slope is less than 1, eliminating choices C and D.

The y-intercept of the line y=mx+b can be found by rearranging the equation and using one of the points we chose.

  b = y - mx

  b = 46 -(3/4)(40) . . . . . . . using (x, y) = (40, 46)

  b = 46 -30 = 16

This value is lower than 19 or 25, the y-intercepts of choices A and B, respectively.

Choice A (green line) is the equation of a line with slightly lower slope than we calculated, and a slightly higher y-intercept. It is the best choice. The attached graph shows choice B (blue line) gives a line well above the plotted points.

The line that best models the plot is y = 2/3x +19, choice A.

B. MPG

For x = 43, the above line gives ...

  y = 2/3x +19

  y = 2/3(43) +19 = 28 2/3 +19 = 47.67

Based on the model, the highway fuel economy would be 47.67 mpg.

View image sqdancefan

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