Answer :
Sure! Let's find the correct trend line equation that matches the data provided.
We are given a table with the following data points:
- (8, 20)
- (8, 18)
- (7, 21)
- (9, ??)
Alex used a regression calculator and found the equation of the trend line to be [tex]\( y = 1.7x + 6.2 \)[/tex], where:
- [tex]\( a = 1.7 \)[/tex]
- [tex]\( b = 6.2 \)[/tex]
Our task is to match this equation with one of the provided options:
1. [tex]\( S = 17f + 6.2 \)[/tex]
2. [tex]\( s = 6.2f + 1.7 \)[/tex]
3. [tex]\( f = 1.7s + 6.2 \)[/tex]
4. [tex]\( f = 6.2s + 1.7 \)[/tex]
First, let's rewrite the equation provided by Alex using the variables given in the options to identify which one fits. The equation [tex]\( y = 1.7x + 6.2 \)[/tex] means:
- [tex]\( y \)[/tex] is the dependent variable (the output of the equation)
- [tex]\( x \)[/tex] is the independent variable (the input of the equation)
To determine which option matches this form, let's compare each:
1. [tex]\( S = 17f + 6.2 \)[/tex]:
- This does not match because of the coefficient and variable [tex]\( S \)[/tex] should be on the left and [tex]\( f \)[/tex] and the constant on the right, but their roles don’t match the [tex]\( y = 1.7x + 6.2 \)[/tex] format.
2. [tex]\( s = 6.2f + 1.7 \)[/tex]:
- Similarly, this does not match our desired structure either.
3. [tex]\( f = 1.7s + 6.2 \)[/tex]:
- Here, [tex]\( f \)[/tex] (which corresponds to [tex]\( y \)[/tex] in our original equation) is expressed as [tex]\( 1.7s + 6.2 \)[/tex]. It matches exactly with [tex]\( y = 1.7x + 6.2 \)[/tex], with [tex]\( f=y \)[/tex] and [tex]\( s=x \)[/tex]. This matches the form perfectly.
4. [tex]\( f = 6.2s + 1.7 \)[/tex]:
- Again, this does not match because the coefficients are swapped.
Based on the above analysis, the correct trend line equation that represents the data is:
[tex]\[ f = 1.7s + 6.2 \][/tex]
So, the correct option is:
[tex]\[ \boxed{3} \][/tex]
I hope this helps! If you have any more questions, feel free to ask.
We are given a table with the following data points:
- (8, 20)
- (8, 18)
- (7, 21)
- (9, ??)
Alex used a regression calculator and found the equation of the trend line to be [tex]\( y = 1.7x + 6.2 \)[/tex], where:
- [tex]\( a = 1.7 \)[/tex]
- [tex]\( b = 6.2 \)[/tex]
Our task is to match this equation with one of the provided options:
1. [tex]\( S = 17f + 6.2 \)[/tex]
2. [tex]\( s = 6.2f + 1.7 \)[/tex]
3. [tex]\( f = 1.7s + 6.2 \)[/tex]
4. [tex]\( f = 6.2s + 1.7 \)[/tex]
First, let's rewrite the equation provided by Alex using the variables given in the options to identify which one fits. The equation [tex]\( y = 1.7x + 6.2 \)[/tex] means:
- [tex]\( y \)[/tex] is the dependent variable (the output of the equation)
- [tex]\( x \)[/tex] is the independent variable (the input of the equation)
To determine which option matches this form, let's compare each:
1. [tex]\( S = 17f + 6.2 \)[/tex]:
- This does not match because of the coefficient and variable [tex]\( S \)[/tex] should be on the left and [tex]\( f \)[/tex] and the constant on the right, but their roles don’t match the [tex]\( y = 1.7x + 6.2 \)[/tex] format.
2. [tex]\( s = 6.2f + 1.7 \)[/tex]:
- Similarly, this does not match our desired structure either.
3. [tex]\( f = 1.7s + 6.2 \)[/tex]:
- Here, [tex]\( f \)[/tex] (which corresponds to [tex]\( y \)[/tex] in our original equation) is expressed as [tex]\( 1.7s + 6.2 \)[/tex]. It matches exactly with [tex]\( y = 1.7x + 6.2 \)[/tex], with [tex]\( f=y \)[/tex] and [tex]\( s=x \)[/tex]. This matches the form perfectly.
4. [tex]\( f = 6.2s + 1.7 \)[/tex]:
- Again, this does not match because the coefficients are swapped.
Based on the above analysis, the correct trend line equation that represents the data is:
[tex]\[ f = 1.7s + 6.2 \][/tex]
So, the correct option is:
[tex]\[ \boxed{3} \][/tex]
I hope this helps! If you have any more questions, feel free to ask.
