Solved on Sep 15, 2023

Determine the better linear equation fit, $y=-2x+4$ or $y=-0.5x+4$ , for the data points $(0,4),(1,2.5),(2,0),(3,-1.5)$ .

STEP 1

Assumptions1. We have two equations, $y=- x+4$ and $y=-0.5 x+4$ . We have four data points $(0,4),(1,.5),(,0),(3,-1.5)$ 3. The better fit will be determined by which equation produces the smallest total difference when each data point is plugged in.

STEP 2

First, we will calculate the total difference for the first equation $y=-2 x+4$ . We do this by plugging each data point into the equation, calculating the difference between the actual y-value and the predicted y-value, and summing these differences.

STEP 3

Plug in the first data point $(0,)$ into the first equation $y=-2 x+$ .
$y = -2(0) +$

STEP 4

Calculate the predicted y-value for the first data point.
$y = -2(0) +4 =4$

STEP 5

Calculate the difference between the actual y-value and the predicted y-value for the first data point.
$Difference = |Actual\, y - Predicted\, y| = |4 -4| =0$

STEP 6

Repeat steps3-5 for the remaining data points $(1,2.5),(2,0),(3,-1.5)$ and sum the differences.

STEP 7

Calculate the total difference for the first equation.
$Total\, difference =0 + |2.5 -2| + |0 -0| + |-1.5 - (-2)| =0.5$

STEP 8

Now, we will calculate the total difference for the second equation $y=-0.5 x+4$ . We do this by plugging each data point into the equation, calculating the difference between the actual y-value and the predicted y-value, and summing these differences.

STEP 9

Plug in the first data point $(,4)$ into the second equation $y=-.5 x+4$ .
$y = -.5() +4$

STEP 10

Calculate the predicted y-value for the first data point.
$y = -0.5(0) +4 =4$

STEP 11

Calculate the difference between the actual y-value and the predicted y-value for the first data point.
$Difference = |Actual\, y - Predicted\, y| = |4 -4| =0$

STEP 12

Repeat steps9-11 for the remaining data points $(,2.5),(2,0),(,-.5)$ and sum the differences.

STEP 13

Calculate the total difference for the second equation.
$Total\, difference =0 + |2.5 -3.5| + |0 -2| + |-.5 - (-0.5)| =3$

STEP 14

Compare the total differences for the two equations. The equation with the smallest total difference is the better fit for the data points.
In this case, the total difference for the first equation $y=-2 x+4$ is0., and the total difference for the second equation $y=-0. x+4$ is3.
Therefore, the first equation $y=-2 x+4$ is the better fit for the data points.
The answer is B. $y=-2 x+4$ .

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Determine the better linear equation fit, $y=-2x+4$ or $y=-0.5x+4$ , for the data points $(0,4),(1,2.5),(2,0),(3,-1.5)$ .

STEP 1

Assumptions1. We have two equations, $y=- x+4$ and $y=-0.5 x+4$ . We have four data points $(0,4),(1,.5),(,0),(3,-1.5)$ 3. The better fit will be determined by which equation produces the smallest total difference when each data point is plugged in.

STEP 2

First, we will calculate the total difference for the first equation $y=-2 x+4$ . We do this by plugging each data point into the equation, calculating the difference between the actual y-value and the predicted y-value, and summing these differences.

STEP 3

Plug in the first data point $(0,)$ into the first equation $y=-2 x+$ .
$y = -2(0) +$

STEP 4

Calculate the predicted y-value for the first data point.
$y = -2(0) +4 =4$

STEP 5

Calculate the difference between the actual y-value and the predicted y-value for the first data point.
$Difference = |Actual\, y - Predicted\, y| = |4 -4| =0$

STEP 6

Repeat steps3-5 for the remaining data points $(1,2.5),(2,0),(3,-1.5)$ and sum the differences.

STEP 7

Calculate the total difference for the first equation.
$Total\, difference =0 + |2.5 -2| + |0 -0| + |-1.5 - (-2)| =0.5$

STEP 8

Now, we will calculate the total difference for the second equation $y=-0.5 x+4$ . We do this by plugging each data point into the equation, calculating the difference between the actual y-value and the predicted y-value, and summing these differences.

STEP 9

Plug in the first data point $(,4)$ into the second equation $y=-.5 x+4$ .
$y = -.5() +4$

STEP 10

Calculate the predicted y-value for the first data point.
$y = -0.5(0) +4 =4$

STEP 11

Calculate the difference between the actual y-value and the predicted y-value for the first data point.
$Difference = |Actual\, y - Predicted\, y| = |4 -4| =0$

STEP 12

Repeat steps9-11 for the remaining data points $(,2.5),(2,0),(,-.5)$ and sum the differences.

STEP 13

Calculate the total difference for the second equation.
$Total\, difference =0 + |2.5 -3.5| + |0 -2| + |-.5 - (-0.5)| =3$

STEP 14

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Determine the better linear equation fit, y=−2x+4y=-2x+4y=−2x+4 or y=−0.5x+4y=-0.5x+4y=−0.5x+4, for the data points (0,4),(1,2.5),(2,0),(3,−1.5)(0,4),(1,2.5),(2,0),(3,-1.5)(0,4),(1,2.5),(2,0),(3,−1.5).

STEP 1

STEP 2

First, we will calculate the total difference for the first equation y=−2x+4y=-2 x+4y=−2x+4. We do this by plugging each data point into the equation, calculating the difference between the actual y-value and the predicted y-value, and summing these differences.

STEP 3

Plug in the first data point (0,)(0,)(0,) into the first equation y=−2x+y=-2 x+y=−2x+.y=−2(0)+y = -2(0) +y=−2(0)+

STEP 4

Calculate the predicted y-value for the first data point.y=−2(0)+4=4y = -2(0) +4 =4y=−2(0)+4=4

STEP 5

Calculate the difference between the actual y-value and the predicted y-value for the first data point.Difference=∣Actual y−Predicted y∣=∣4−4∣=0Difference = |Actual\, y - Predicted\, y| = |4 -4| =0Difference=∣Actualy−Predictedy∣=∣4−4∣=0

STEP 6

Repeat steps3-5 for the remaining data points (1,2.5),(2,0),(3,−1.5)(1,2.5),(2,0),(3,-1.5)(1,2.5),(2,0),(3,−1.5) and sum the differences.

STEP 7

Calculate the total difference for the first equation.Total difference=0+∣2.5−2∣+∣0−0∣+∣−1.5−(−2)∣=0.5Total\, difference =0 + |2.5 -2| + |0 -0| + |-1.5 - (-2)| =0.5Totaldifference=0+∣2.5−2∣+∣0−0∣+∣−1.5−(−2)∣=0.5

STEP 8

Now, we will calculate the total difference for the second equation y=−0.5x+4y=-0.5 x+4y=−0.5x+4. We do this by plugging each data point into the equation, calculating the difference between the actual y-value and the predicted y-value, and summing these differences.

STEP 9

Plug in the first data point (,4)(,4)(,4) into the second equation y=−.5x+4y=-.5 x+4y=−.5x+4.y=−.5()+4y = -.5() +4y=−.5()+4

STEP 10

Calculate the predicted y-value for the first data point.y=−0.5(0)+4=4y = -0.5(0) +4 =4y=−0.5(0)+4=4

STEP 11

Calculate the difference between the actual y-value and the predicted y-value for the first data point.Difference=∣Actual y−Predicted y∣=∣4−4∣=0Difference = |Actual\, y - Predicted\, y| = |4 -4| =0Difference=∣Actualy−Predictedy∣=∣4−4∣=0

STEP 12

Repeat steps9-11 for the remaining data points (,2.5),(2,0),(,−.5)(,2.5),(2,0),(,-.5)(,2.5),(2,0),(,−.5) and sum the differences.

STEP 13

Calculate the total difference for the second equation.Total difference=0+∣2.5−3.5∣+∣0−2∣+∣−.5−(−0.5)∣=3Total\, difference =0 + |2.5 -3.5| + |0 -2| + |-.5 - (-0.5)| =3Totaldifference=0+∣2.5−3.5∣+∣0−2∣+∣−.5−(−0.5)∣=3

STEP 14

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Determine the better linear equation fit, $y=-2x+4$ or $y=-0.5x+4$ , for the data points $(0,4),(1,2.5),(2,0),(3,-1.5)$ .

First, we will calculate the total difference for the first equation $y=-2 x+4$ . We do this by plugging each data point into the equation, calculating the difference between the actual y-value and the predicted y-value, and summing these differences.

Plug in the first data point $(0,)$ into the first equation $y=-2 x+$ .
$y = -2(0) +$

Calculate the predicted y-value for the first data point.
$y = -2(0) +4 =4$

Calculate the difference between the actual y-value and the predicted y-value for the first data point.
$Difference = |Actual\, y - Predicted\, y| = |4 -4| =0$

Repeat steps3-5 for the remaining data points $(1,2.5),(2,0),(3,-1.5)$ and sum the differences.

Calculate the total difference for the first equation.
$Total\, difference =0 + |2.5 -2| + |0 -0| + |-1.5 - (-2)| =0.5$

Now, we will calculate the total difference for the second equation $y=-0.5 x+4$ . We do this by plugging each data point into the equation, calculating the difference between the actual y-value and the predicted y-value, and summing these differences.

Plug in the first data point $(,4)$ into the second equation $y=-.5 x+4$ .
$y = -.5() +4$

Calculate the predicted y-value for the first data point.
$y = -0.5(0) +4 =4$

Calculate the difference between the actual y-value and the predicted y-value for the first data point.
$Difference = |Actual\, y - Predicted\, y| = |4 -4| =0$

Repeat steps9-11 for the remaining data points $(,2.5),(2,0),(,-.5)$ and sum the differences.

Calculate the total difference for the second equation.
$Total\, difference =0 + |2.5 -3.5| + |0 -2| + |-.5 - (-0.5)| =3$