To find the equation of the line passing through two given points $(-4, 6)$ and $(3, -1)$, we use the point-slope form of the equation of a line:

Step 1: Find the slope ($m$)

The slope formula is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substitute the coordinates: $m = \frac{-1 - 6}{3 - (-4)} = \frac{-7}{7} = -1$

Step 2: Use the point-slope form

The point-slope form is: $y - y_1 = m(x - x_1)$ Using the slope $m = -1$ and one of the points (e.g., $(-4, 6)$): $y - 6 = -1(x - (-4))$

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

Simplify: $y - 6 = -1(x + 4)$ $y - 6 = -x - 4$ $y = -x + 2$

Final Answer:

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

Let me know if you’d like a detailed explanation of any step!

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5 Related Questions:

1. How do you find the slope of a line given two points?
2. Can you rewrite the equation $y = -x + 2$ in standard form?
3. What is the y-intercept of the line $y = -x + 2$?
4. How do you find the equation of a line parallel to this one through a different point?
5. What is the equation of a line perpendicular to this one that passes through $(3, -1)$?

Tip: Always verify the equation by plugging the points into it to ensure they satisfy the equation!