Find the equation (in terms of x) of the line through the points (-3,-2) and (4,0)

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To find the equation of the line passing through two points, we use the point-slope form of a line, given by:

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

where \( m \) is the slope of the line, and \( (x_1, y_1) \) is one of the points on the line.

1. **Calculate the Slope (m):**

   For two points \((x_1, y_1)\) and \((x_2, y_2)\), the slope \( m \) is:

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

   Given points \((-3, -2)\) and \((4, 0)\):

   \[
   m = \frac{0 - (-2)}{4 - (-3)} = \frac{2}{7}
   \]

2. **Write the Equation of the Line:**

   Using point-slope form with the point \((-3, -2)\):

   \[
   y - (-2) = \frac{2}{7}(x - (-3))
   \]

   Simplifying:

   \[
   y + 2 = \frac{2}{7}(x + 3)
   \]

3. **Convert to Slope-Intercept Form \(y = mx + b\):**

   Distribute and simplify:

   \[
   y + 2 = \frac{2}{7}x + \frac{6}{7}
   \]

   \[
   y = \frac{2}{7}x + \frac{6}{7} - 2
   \]

   \[
   y = \frac{2}{7}x - \frac{8}{7}
   \]

Thus, the equation of the line is:

\[
y = \frac{2}{7}x - \frac{8}{7}
\]

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### Related Questions

1. How do you convert from point-slope form to slope-intercept form?
2. What is the importance of slope in defining a line?
3. How can you verify if a given point lies on a line?
4. How do you find the midpoint between two points on a line?
5. How would the equation change if the line were vertical or horizontal?

**Tip:** Remember, if two points have the same x-coordinate, the line between them is vertical, and if they share the same y-coordinate, it’s horizontal.

Find the equation (in terms of x) of the line through the points (-3,-2) and (4,0)

Learn how to find the equation of a line passing through points (-3,-2) and (4,0) using key concepts in algebra and coordinate geometry. This guide provides a step-by-step approach to calculating the slope, using point-slope form, and converting to slope-intercept form, suitable for students in Grades 8-10.

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