find the equation of the point (-9,3) and (3,9)

To find the equation of the line that passes through the points \((-9, 3)\) and \((3, 9)\), follow these steps:

### 1. Find the slope (\(m\)) of the line.
The slope formula is:

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

For the points \((-9, 3)\) and \((3, 9)\), let:
- \((x_1, y_1) = (-9, 3)\)
- \((x_2, y_2) = (3, 9)\)

Substitute these values into the slope formula:

\[
m = \frac{9 - 3}{3 - (-9)} = \frac{6}{12} = \frac{1}{2}
\]

### 2. Use the point-slope form of the line equation.
The point-slope form is:

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

Using the point \((-9, 3)\) and the slope \(m = \frac{1}{2}\), substitute into the equation:

\[
y - 3 = \frac{1}{2}(x - (-9))
\]

Simplify:

\[
y - 3 = \frac{1}{2}(x + 9)
\]

### 3. Solve for \(y\) to put it in slope-intercept form.
Distribute the \(\frac{1}{2}\):

\[
y - 3 = \frac{1}{2}x + \frac{9}{2}
\]

Add \(3\) to both sides (convert \(3\) to a fraction):

\[
y = \frac{1}{2}x + \frac{9}{2} + \frac{6}{2}
\]

\[
y = \frac{1}{2}x + \frac{15}{2}
\]

### Final equation:
The equation of the line is:

\[
y = \frac{1}{2}x + \frac{15}{2}
\]

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Would you like more details or have any questions?

Here are 5 related questions:
1. How do you find the equation of a line given two points?
2. What is the significance of the slope in a line equation?
3. Can you explain point-slope form and when to use it?
4. How do you convert a line equation from point-slope form to slope-intercept form?
5. What are other forms of linear equations, and how are they used?

**Tip:** Always double-check your slope calculations when finding a line equation to ensure accuracy.

Learn how to find the equation of a line passing through the points (-9,3) and (3,9) with a step-by-step solution. This problem involves key algebraic concepts such as slope calculation, point-slope form, and slope-intercept form. Suitable for students in Grades 8-10.

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