To find the slope-intercept form of the equation of the line passing through the points $(-9, 7)$ and $(9, 1)$, we follow these steps:

Step 1: Find the slope (m) using the formula:

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

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

Step 2: Use the point-slope form of the line equation:

The point-slope form is: $y - y_1 = m(x - x_1)$

Using one of the points, say $(-9, 7)$, and the slope $m = -\frac{1}{3}$: $y - 7 = -\frac{1}{3}(x - (-9))$ $y - 7 = -\frac{1}{3}(x + 9)$

Step 3: Simplify to slope-intercept form ($y = mx + b$):

Distribute the slope: $y - 7 = -\frac{1}{3}x - 3$

Add 7 to both sides: $y = -\frac{1}{3}x + 4$

Final Answer:

The slope-intercept form of the equation of the line is: $y = -\frac{1}{3}x + 4$

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Would you like to see the steps explained further or any other clarifications?

Related Questions:

1. How do you verify the equation works for both points?
2. What is the significance of the slope in this line?
3. How would the equation change if the points were swapped?
4. How can this be graphed using the slope and intercept?
5. What are real-world applications of finding equations of lines?

Tip: Always simplify the slope before substituting into the point-slope formula to avoid errors.