To find the equation of the line passing through the points $(-9, 7)$ and $(9, 1)$ in slope-intercept form ($y = mx + b$), follow these steps:

Step 1: Find the slope ($m$):

The slope formula is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substitute the points $(-9, 7)$ and $(9, 1)$:

$m = \frac{1 - 7}{9 - (-9)} = \frac{-6}{18} = -\frac{1}{3}$

Step 2: Use the slope-intercept form ($y = mx + b$):

Start with $y = -\frac{1}{3}x + b$. We need to find $b$ (the y-intercept).

Step 3: Substitute one point into the equation to solve for $b$:

Using the point $(-9, 7)$:

$7 = -\frac{1}{3}(-9) + b$

Simplify:

$7 = 3 + b$

$b = 4$

Final Equation:

The equation of the line in slope-intercept form is:

$y = -\frac{1}{3}x + 4$

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Would you like a detailed graph or further explanations?
Here are some related questions to consider:

1. How do you find the equation of a line given its slope and one point?
2. What is the importance of slope-intercept form in geometry?
3. How would you rewrite this equation in standard form?
4. What are the steps to find the distance between these two points?
5. Can you verify the equation by substituting both points?

Tip: Always double-check the slope calculation to avoid errors when solving linear equations.