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.