To find the relationship between \( g \) and \( h \), we can analyze the data provided:
\[ \begin{array}{|c|c|} \hline g & h \ \hline 4 & 21 \ 5 & 22 \ 6 & 23 \ 7 & 24 \ \hline \end{array} \]
Observing the values of \( g \) and \( h \):
- When \( g = 4 \), \( h = 21 \)
- When \( g = 5 \), \( h = 22 \)
- When \( g = 6 \), \( h = 23 \)
- When \( g = 7 \), \( h = 24 \)
From this, we can see that \( h \) increases by 1 for each increase of 1 in \( g \). Therefore, the relationship appears to be linear.
To derive the equation, we can observe that when \( g = 4 \), \( h \) is 21. So we can use this point to establish the equation in the form:
\[ h = g + b \]
To find \( b \) when \( g = 4\):
\[ 21 = 4 + b \] \[ b = 21 - 4 \] \[ b = 17 \]
Now we can generalize the relationship:
\[ h = g + 17 \]
To verify, we can substitute the values of \( g \):
- For \( g = 4 \): \( h = 4 + 17 = 21 \)
- For \( g = 5 \): \( h = 5 + 17 = 22 \)
- For \( g = 6 \): \( h = 6 + 17 = 23 \)
- For \( g = 7 \): \( h = 7 + 17 = 24 \)
The equation correctly predicts all the \( h \) values.
So, the relationship between \( g \) and \( h \) can be expressed as:
\[ h = g + 17 \]