To find the equation of the line passing through the points $(-4, 6)$ and $(1, 1)$, follow these steps:

Step 1: Find the slope of the line

The formula for the slope, $m$, is: $m = \frac{y_2 - y_1}{x_2 - x_1}$

Substitute the given points $(x_1, y_1) = (-4, 6)$ and $(x_2, y_2) = (1, 1)$: $m = \frac{1 - 6}{1 - (-4)} = \frac{-5}{1 + 4} = \frac{-5}{5} = -1$

So, the slope $m = -1$.

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

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

Substitute $m = -1$ and one of the points, such as $(-4, 6)$: $y - 6 = -1(x - (-4))$ $y - 6 = -1(x + 4)$

Simplify: $y - 6 = -x - 4$ $y = -x + 2$

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Final Answer:

The equation of the line is: $y = -x + 2$

Let me know if you'd like further explanation!

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Related Questions:

1. What is the slope of the line passing through $(2, 3)$ and $(4, 7)$?
2. How do you convert a line equation in point-slope form to slope-intercept form?
3. What is the significance of the slope in a line equation?
4. Can you find the equation of a vertical line passing through a given point?
5. What is the general formula for finding the slope between two points?

Tip:

Always double-check your slope calculation when working with negative values to avoid sign errors.