Zefram analyzed a linear relationship, found that the slope-intercept equation was
y 3.5x 16
, and
made a prediction for the value of
y
for a given value of
x.
He realized that he made an error calculating
the y-intercept and that it was actually 12. Can he just subtract 4 from his prediction if he knows that the
slope is correct? Explain.
oof u
No, Zefram cannot simply subtract 4 from his prediction in this situation.
To understand why, let's first clarify the meaning of the slope-intercept equation he analyzed:
y = 3.5x + 16
In this equation, the number in front of the variable x (3.5) is the slope of the line, and the number at the end (16) is the y-intercept. The y-intercept represents the value of y when x is 0.
Now, as Zefram realized he made an error in calculating the y-intercept, he found that it should have been 12 instead of 16. This means the correct slope-intercept equation should be:
y = 3.5x + 12
If Zefram wants to make a prediction for a given value of x using this corrected equation, he needs to substitute that value of x into the equation and solve for y. He cannot simply subtract 4 from his previous prediction.
Let's say Zefram's previous prediction was y = 30 for a given value of x. If he subtracts 4 from this value, he would get y = 26. However, this new value does not follow the corrected equation because it does not account for the error in the y-intercept.
To make a correct prediction using the corrected slope-intercept equation, Zefram should substitute the given value of x into the equation as follows:
y = 3.5x + 12
For example, if x = 5, then the prediction would be:
y = 3.5(5) + 12
y = 17.5 + 12
y = 29.5
Therefore, Zefram should use the corrected equation to make his predictions and not simply subtract 4 from his previous predictions.