Respuesta :
We are asked to determine a linear model that relates the time and height of a person.
Let "x" be the time since birth and "y" the height, then we are given the following points:
[tex]\begin{gathered} (x_1,y_1)=(0,24in) \\ (x_2,y_2)=(10,4\text{feet)} \end{gathered}[/tex]Now, we convert the inches to feet using the following conversion factor:
[tex]1\text{feet}=12in[/tex]Now, we multiply by the conversion factor:
[tex]24in\times\frac{1\text{feet}}{12in}=2feet[/tex]Therefore, the points are:
[tex]\begin{gathered} (x_1,y_1)=(0,2feet) \\ (x_2,y_2)=(10,4\text{feet)} \end{gathered}[/tex]Now, we determine the slope of the line using the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Substituting the values we get:
[tex]m=\frac{4-2}{10-0}=\frac{2}{10}=\frac{1}{5}[/tex]Now, we use the general form of a line equation in slope-intercept form:
[tex]y=mx+b[/tex]Where "m" is the slope and "b" is the y-intercept. Now, we substitute the value of the slope:
[tex]y=\frac{1}{5}x+b[/tex]To determine the value of "b" we will substitute the first point:
[tex]2=\frac{1}{5}(0)+b[/tex]Solving the operations:
[tex]2=b[/tex]Therefore, the value of "b" is 2:
[tex]y=\frac{1}{5}x+2[/tex]Now, we substitute the value "x= 9", we get:
[tex]\begin{gathered} y=\frac{1}{5}(9)+2 \\ \end{gathered}[/tex]Solving the operations:
[tex]y=3.8[/tex]Therefore, the height at age 9 is 3.8 feet.
