To find the equation of the line passing through the points $(6, -3)$ and $(3, 1)$, we follow these steps:

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Step 1: Find the slope of the line

The formula for the slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

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

Substitute the given points $(6, -3)$ and $(3, 1)$:

$m = \frac{1 - (-3)}{3 - 6} = \frac{1 + 3}{-3} = \frac{4}{-3} = -\frac{4}{3}$

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

The point-slope form is:

$y - y_1 = m(x - x_1)$

Choose one of the points, say $(6, -3)$, and substitute $m = -\frac{4}{3}$, $x_1 = 6$, and $y_1 = -3$:

$y - (-3) = -\frac{4}{3}(x - 6)$

Simplify:

$y + 3 = -\frac{4}{3}(x - 6)$

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Step 3: Simplify to slope-intercept form (optional)

Distribute the slope:

$y + 3 = -\frac{4}{3}x + 8$

Subtract 3 from both sides:

$y = -\frac{4}{3}x + 5$

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Final Answer

The equation of the line is:

$y = -\frac{4}{3}x + 5$

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Do you want a detailed explanation of the steps or have any further questions?

Related Questions

1. How do you find the slope of a vertical line?
2. What are the differences between point-slope and slope-intercept forms?
3. Can a line have a slope of zero? What does that mean?
4. How can you check if a point lies on a given line?
5. How do you derive the equation of a line in standard form?

Tip

Always double-check slope calculations by verifying the order of subtraction for the coordinates.