Let's determine the correct equation that models the height of the plant [tex]\( y \)[/tex] after [tex]\( x \)[/tex] days based on the given data.
1. Identify the given data:
- After 10 days ([tex]\( x_1 = 10 \)[/tex]), the plant is 30 centimeters tall ([tex]\( y_1 = 30 \)[/tex]).
- After 20 days ([tex]\( x_2 = 20 \)[/tex]), the plant is 50 centimeters tall ([tex]\( y_2 = 50 \)[/tex]).
2. Calculate the slope (rate of growth) of the plant:
- The slope [tex]\( m \)[/tex] is calculated using the formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
- Substituting the given values:
[tex]\[
m = \frac{50 - 30}{20 - 10} = \frac{20}{10} = 2
\][/tex]
3. Find the equation in point-slope form:
- The point-slope form of a linear equation is:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
- Using the point [tex]\((x_1, y_1) = (10, 30)\)[/tex] and the slope [tex]\( m = 2 \)[/tex], the equation becomes:
[tex]\[
y - 30 = 2(x - 10)
\][/tex]
Therefore, the equation that models the height of the plant [tex]\( y \)[/tex] after [tex]\( x \)[/tex] days is:
[tex]\[ y - 30 = 2(x - 10) \][/tex]
So the correct answer is:
[tex]\[ \boxed{A. \, y - 30 = 2(x - 10)} \][/tex]
