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solve for point slope and slope intercept

To solve for the point-slope form and slope-intercept form based on the table provided in the image, we need to follow these steps:

### Table dataTo solve for the point-slope form and slope-intercept form based on the table provided in the image, we need to follow these steps:

### Table 
The table shows pairs of \(x\) and \(y\) values:

\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
15 & 100 \\
20 & 115 \\
25 & 130 \\
30 & 145 \\
35 & 160 \\
\hline
\end{array}
\]

### Step 1: Calculate the slope (\(m\))
The slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated as:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

We can choose any two points, for example:
- \( (15, 100) \) and \( (20, 115) \)

Substitute these values into the formula for the slope:

\[
m = \frac{115 - 100}{20 - 15} = \frac{15}{5} = 3
\]

So, the slope is \( m = 3 \).

### Step 2: Point-Slope Form
The point-slope form of a line is:

\[
y - y_1 = m(x - x_1)
\]

Using the point \( (15, 100) \) and the slope \( m = 3 \):

\[
y - 100 = 3(x - 15)
\]

This is the point-slope form of the equation.

### Step 3: Slope-Intercept Form
To convert the point-slope form to the slope-intercept form \( y = mx + b \), we simplify the equation:

\[
y - 100 = 3(x - 15)
\]
\[
y - 100 = 3x - 45
\]
\[
y = 3x - 45 + 100
\]
\[
y = 3x + 55
\]

So, the slope-intercept form is:

\[
y = 3x + 55
\]

### Summary:
- **Point-Slope Form:** \( y - 100 = 3(x - 15) \)
- **Slope-Intercept Form:** \( y = 3x + 55 \)

Let me know if you'd like more details or have any questions.

Here are 5 relative questions:
1. How do you find the slope from a table of values?
2. What does the slope represent in a linear relationship?
3. How do you interpret the y-intercept in the slope-intercept form?
4. Can you find the equation of the line using any two points from the table?
5. How would the equation change if the slope was negative?

**Tip:** When calculating slope, always double-check the differences in \(y\) and \(x\) to ensure accuracy.

This guide provides a step-by-step solution for solving the point-slope form and slope-intercept form of a linear equation using a table of values. The example uses pairs of x and y values such as (15, 100) and (20, 115) to calculate the slope and formulate both forms of the line equation. Suitable for students in Grades 8-10.

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