To write the equation of the line passing through the given 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 given points: $m = \frac{1 - 7}{9 - (-9)} = \frac{-6}{18} = -\frac{1}{3}$

Step 2: Use the slope and a point to find the y-intercept ($b$)

The slope-intercept form is: $y = mx + b$

Substitute $m = -\frac{1}{3}$ and one of the points, say $(-9, 7)$, into the equation: $7 = -\frac{1}{3}(-9) + b$

Simplify: $7 = 3 + b$

Solve for $b$: $b = 7 - 3 = 4$

Step 3: Write the equation

Now that we know the slope ($m = -\frac{1}{3}$) and the y-intercept ($b = 4$), the equation of the line is: $y = -\frac{1}{3}x + 4$

Final Answer:

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

Would you like more explanation or have any other questions?

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Here are 5 related questions to expand your understanding:

1. How would you find the equation of a vertical line passing through these points?
2. Can you convert this equation to standard form?
3. What are the x-intercept and y-intercept of this line?
4. How do you verify that both points lie on the line?
5. How would the slope change if the order of the points were reversed?

Tip: Always simplify fractions and verify calculations when working with slope formulas!