To determine when both plants will reach the same height, we need to set the two equations equal to each other and solve for \( x \). The equations representing the plants' heights are:
[tex]\[ \text{Plant A: } y = 1.8x + 3.1 \][/tex]
[tex]\[ \text{Plant B: } y = 2.3x + 1.9 \][/tex]
We set the equations equal to each other to find the point where the heights are the same:
[tex]\[ 1.8x + 3.1 = 2.3x + 1.9 \][/tex]
Next, we solve for \( x \):
1. Subtract \( 1.8x \) from both sides:
[tex]\[ 3.1 = 2.3x - 1.8x + 1.9 \][/tex]
[tex]\[ 3.1 = 0.5x + 1.9 \][/tex]
2. Subtract \( 1.9 \) from both sides:
[tex]\[ 3.1 - 1.9 = 0.5x \][/tex]
[tex]\[ 1.2 = 0.5x \][/tex]
3. Divide both sides by 0.5:
[tex]\[ x = \frac{1.2}{0.5} \][/tex]
[tex]\[ x = 2.4 \][/tex]
Therefore, it will take approximately 2.4 weeks for both plants to reach the same height. Rounding this to the nearest tenth confirms our answer.
So, the correct option is:
[tex]\[ \boxed{2.4 \text{ weeks}} \][/tex]
