Given the information in the table, we can calculate the slope of the line using the equation:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Where x₁ and x₂ are the months number 3 and 8, respectively. y₁ and y₂ are the lengths of the hair in those months. Then:
[tex]\begin{gathered} \text{Friend}\colon m_F=\frac{6.5-4}{8-3}=\frac{2.5}{5}=0.5 \\ \text{Cou}\sin \colon m_C=\frac{9-7}{8-3}=\frac{2}{5}=0.4 \end{gathered}[/tex]
Now, using the point-slope form of the equation of the line:
[tex]\begin{gathered} \text{Friend}\colon y-4=m_F(x-3)\Rightarrow y=0.5x+2.5_{} \\ \text{Cousin}\colon y-7=m_C(x-3)\Rightarrow y=0.4x+5.8 \end{gathered}[/tex]
To calculate if their hair length would ever be equal, we use the equations above:
[tex]\begin{gathered} 0.5x+2.5=0.4x+5.8 \\ 0.1x=3.3 \\ x=33 \end{gathered}[/tex]
They will be equal after 33 months.
