Find the slope intercept form equation for the line.

The line through the points: (4, 2) and (- 3, 1)

To find the slope-intercept form equation of the line passing through the points \( (4, 2) \) and \( (-3, 1) \), follow these steps:

### Step 1: Find the slope of the line
The slope \( m \) of the line through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

Substituting the given points \( (4, 2) \) and \( (-3, 1) \):

\[
m = \frac{1 - 2}{-3 - 4} = \frac{-1}{-7} = \frac{1}{7}
\]

### Step 2: Use the point-slope form to find the equation of the line
The point-slope form of a line is:

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

Using the point \( (4, 2) \) and the slope \( m = \frac{1}{7} \):

\[
y - 2 = \frac{1}{7}(x - 4)
\]

### Step 3: Simplify to obtain the slope-intercept form
Expand and simplify the equation:

\[
y - 2 = \frac{1}{7}x - \frac{4}{7}
\]

Add 2 to both sides:

\[
y = \frac{1}{7}x - \frac{4}{7} + \frac{14}{7}
\]

Simplify further:

\[
y = \frac{1}{7}x + \frac{10}{7}
\]

### Final Answer: Slope-Intercept Form
The equation of the line in slope-intercept form is:

\[
\boxed{y = \frac{1}{7}x + \frac{10}{7}}
\]

Would you like more details on any step, or do you have any questions?

### Related Questions
1. How do you convert the slope-intercept form to the general form equation?
2. What does the y-intercept represent in the equation of a line?
3. How can you find the equation of a line given the slope and one point?
4. What is the significance of the slope in a linear equation?
5. How do you find the equation of a line parallel or perpendicular to a given line?

### Tip
When working with fractions in the slope-intercept form, be careful to simplify correctly, especially when combining fractions or adding constants.

Learn how to find the slope-intercept form equation of a line passing through the points (4, 2) and (-3, 1). This problem involves calculating the slope using the slope formula, applying the point-slope form, and converting it to the slope-intercept form. Suitable for students in Grades 7-9.

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