To find the equation of the line that passes through the given points [tex]\((7, 3)\)[/tex], [tex]\((14, 6)\)[/tex], and [tex]\((21, 9)\)[/tex], we can use the concept of the slope.
First, let’s determine the slope of the line. The formula for the slope [tex]\( m \)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Using the points [tex]\((7, 3)\)[/tex] and [tex]\((14, 6)\)[/tex]:
[tex]\[
x_1 = 7, \quad y_1 = 3, \quad x_2 = 14, \quad y_2 = 6
\][/tex]
Substitute these values into the slope formula:
[tex]\[
m = \frac{6 - 3}{14 - 7} = \frac{3}{7}
\][/tex]
Now that we have the slope, we know that the equation of the line in slope-intercept form is:
[tex]\[ y = mx + b \][/tex]
Given that the problem options are in the form where the y-intercept [tex]\( b \)[/tex] is 0, we look for the equation [tex]\( y = mx \)[/tex]. Since we’ve calculated the slope [tex]\( m = \frac{3}{7} \)[/tex], the equation of the line becomes:
[tex]\[ y = \frac{3}{7} x \][/tex]
This corresponds to option A.
Therefore, the equation of the line containing the points [tex]\((7, 3)\)[/tex], [tex]\((14, 6)\)[/tex], and [tex]\((21, 9)\)[/tex] is:
[tex]\[ \boxed{y = \frac{3}{7} x} \][/tex]
