For a science experiment, Mala measured the height of a plant every week. She recorded that the growth is linear. Write an equation in point-slope form to represent the information in the table.

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To write an equation in **point-slope form** for Mala's plant growth data, you'll need the following information from the table:

1. **A specific data point $$(x_1, y_1)$$:** This represents the plant's height at a particular week.
2. **The slope $$m$$:** This indicates the rate of growth per week.

**Point-Slope Form Equation:**
$$
y - y_1 = m(x - x_1)
$$

**Steps to Create the Equation:**

1. **Identify Two Points from the Table:**
   - For example, suppose the table has the following data:
     $$
     \begin{array}{|c|c|}
     \hline
     \text{Week } (x) & \text{Height (cm) } (y) \
     \hline
     1 & 5 \
     4 & 14 \
     \hline
     \end{array}
     $$
   
2. **Calculate the Slope $$m$$:**
   $$
   m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{14 - 5}{4 - 1} = \frac{9}{3} = 3 \, \text{cm/week}
   $$
   
3. **Choose One Point to Use in the Equation:**
   - Let's use the first point $$(1, 5)$$.
   
4. **Plug the Values into the Point-Slope Form:**
   $$
   y - 5 = 3(x - 1)
   $$

**Final Equation:**
$$
y - 5 = 3(x - 1)
$$

**Interpretation:**
- **$$m = 3$$:** The plant grows by 3 cm each week.
- **$$(1, 5)$$:** At week 1, the plant was 5 cm tall.

This equation allows you to predict the plant's height at any week $$x$$. For example, to find the height at week 2:
$$
y - 5 = 3(2 - 1) \
y - 5 = 3 \
y = 8 \, \text{cm}
$$

**Note:** If you have different data points in your table, you can follow the same steps to derive the specific point-slope form equation for Mala's experiment.
To represent Mala's plant growth data with a linear equation in point-slope form, use the formula: $$ y - y_1 = m(x - x_1) $$ Where: - $$ (x_1, y_1) $$ is a specific data point from the table. - $$ m $$ is the slope representing the growth rate per week. **Example:** If at week 1 the plant is 5 cm tall and grows at 3 cm per week, the equation is: $$ y - 5 = 3(x - 1) $$ This equation allows you to predict the plant's height at any given week.

For a science experiment, Mala measured the height of a plant every week. She recorded that the growth is linear. Write an equation in point-slope form to represent the information in the table.

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