Question

the equation of the line is ( yapprox - 1.02x + 7.09 ). using the line, she predicted that when the value of ( x ) is ( 0.5 ), the value of ( y ) will be approximately ( 7.6 ). what was her mistake? she drew the line of best fit incorrectly. she used the line of best fit to predict ( y ) for an incorrect value of ( x ). she forgot the minus sign before the first term on the right side of the equation when she predicted ( y ). she plugged ( 0.5 ) into the equation for ( y ) instead of ( x ) and actually predicted ( x ) instead of ( y ).

Explanation:

Step1: Substitute \(x = 0.5\) into the equation \(y\approx - 1.02x + 7.09\)

$$y\approx-1.02\times0.5 + 7.09$$

Step2: Calculate the value of \(y\)

First, calculate \(-1.02\times0.5=-0.51\). Then \(y\approx-0.51 + 7.09 = 6.58\approx6.6
eq7.6\).
If we wrongly substitute \(y = 0.5\) into \(y=-1.02x + 7.09\) and solve for \(x\):
$$0.5=-1.02x + 7.09$$
$$1.02x=7.09 - 0.5$$
$$1.02x = 6.59$$
$$x=\frac{6.59}{1.02}\approx6.46\approx6.5$$. But if we reverse \(x\) and \(y\) (plug \(x = 0.5\) as \(y\) value into wrong variable substitution), assume she did \(x=-1.02y+7.09\), when \(y = 0.5\), \(x=-1.02\times0.5+7.09 = 6.58\approx6.6\) (wrong way of substitution). The correct way is \(y=-1.02x + 7.09\), when \(x = 0.5\), \(y=-1.02\times0.5+7.09=6.58\approx6.6\). The error is due to wrong variable substitution.

Answer:

She plugged \(0.5\) into the equation for \(y\) instead of \(x\) and actually predicted \(x\) instead of \(y\).