To find the equation of a line passing through the points $(-1,6)$ and $(2,0)$, we use the slope-intercept form of a line equation:

$y = mx + b$

Step 1: Find the slope ($m$)

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

Substitute the coordinates: $m = \frac{0 - 6}{2 - (-1)} = \frac{-6}{2 + 1} = \frac{-6}{3} = -2$

Step 2: Use the point-slope formula

The point-slope formula is: $y - y_1 = m(x - x_1)$ Using the slope $m = -2$ and one of the points, say $(-1,6)$: $y - 6 = -2(x - (-1))$ Simplify: $y - 6 = -2(x + 1)$ $y - 6 = -2x - 2$ $y = -2x + 4$

Final Equation

The equation of the line is: $y = -2x + 4$

Verification

To confirm, substitute the other point $(2,0)$ into the equation: $y = -2(2) + 4 = -4 + 4 = 0$ This verifies that the equation is correct.

Would you like more details or further examples?

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Related Questions

1. How do you determine the slope between any two points?
2. What is the process for converting point-slope form to slope-intercept form?
3. How would the equation change if the points were $(-1,6)$ and $(2,1)$?
4. Can you find the perpendicular line passing through one of these points?
5. What is the significance of the slope in real-world applications?

Tip: Always double-check calculations when dealing with signs (e.g., negative and positive) in slope formulas!