write an equation for the line containing points (-2,5) and (2,13)

To find the equation of the line passing through the points \((-2, 5)\) and \((2, 13)\), we can follow these steps:

1. **Find the slope** using the formula for slope between two points:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]
   Here, \((x_1, y_1) = (-2, 5)\) and \((x_2, y_2) = (2, 13)\), so:
   \[
   m = \frac{13 - 5}{2 - (-2)} = \frac{8}{4} = 2
   \]
   The slope \(m = 2\).

2. **Use the point-slope form** of the equation of a line:
   \[
   y - y_1 = m(x - x_1)
   \]
   Using \((x_1, y_1) = (-2, 5)\) and \(m = 2\), the equation becomes:
   \[
   y - 5 = 2(x - (-2)) = 2(x + 2)
   \]

3. **Simplify the equation**:
   \[
   y - 5 = 2x + 4
   \]
   \[
   y = 2x + 9
   \]

Thus, the equation of the line is:
\[
y = 2x + 9
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you calculate the slope if given two different points?
2. Can you convert the slope-intercept form to the standard form?
3. How does the slope of a line relate to its steepness?
4. What happens to the equation if the two points are the same?
5. How do you determine if two lines are parallel?

**Tip:** The slope is a measure of how much the \(y\)-value changes for a given change in the \(x\)-value.

Learn how to find the equation of a line passing through the points (-2,5) and (2,13) using the slope formula and point-slope form. This problem helps students understand core concepts of algebra, including calculating slope and converting to slope-intercept form. Suitable for students in Grades 8-10.

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