To find the equation of the line that passes through the points $(-2, 7)$ and $(3, -8)$, we will use the point-slope form of a line and calculate the slope first.

Step 1: Calculate the slope ($m$)

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

Substitute the points $(-2, 7)$ as $(x_1, y_1)$ and $(3, -8)$ as $(x_2, y_2)$: $m = \frac{-8 - 7}{3 - (-2)} = \frac{-8 - 7}{3 + 2} = \frac{-15}{5} = -3$

Step 2: Use the point-slope form

The point-slope form of the equation of a line is: $y - y_1 = m(x - x_1)$

Using the slope $m = -3$ and one of the points, say $(-2, 7)$: $y - 7 = -3(x - (-2))$ Simplify: $y - 7 = -3(x + 2)$ $y - 7 = -3x - 6$ $y = -3x + 1$

Final Equation

The equation of the line in slope-intercept form is: $y = -3x + 1$

Would you like me to explain further or verify with the second point?

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5 Related Questions:

1. How do you find the equation of a line if the slope and one point are given?
2. Can you rewrite this equation in standard form $Ax + By = C$?
3. How do you determine if two lines are parallel or perpendicular?
4. How would you graph this line using its equation?
5. What happens if you only know the $x$- and $y$-intercepts of a line?

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