To find the equation of a line passing through two points $(-5, 11)$ and $(5, -7)$, we can follow these steps:

Step 1: Calculate the slope $m$

The slope of a line through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substitute the values of the points $(-5, 11)$ and $(5, -7)$: $m = \frac{-7 - 11}{5 - (-5)} = \frac{-18}{5 + 5} = \frac{-18}{10} = -\frac{9}{5}$

Step 2: Use the point-slope form

The equation of a line in point-slope form is: $y - y_1 = m(x - x_1)$ We can use either of the points. Let's use $(-5, 11)$. Substituting the slope and the point: $y - 11 = -\frac{9}{5}(x - (-5))$ Simplify: $y - 11 = -\frac{9}{5}(x + 5)$ Distribute the slope: $y - 11 = -\frac{9}{5}x - 9$ Add 11 to both sides: $y = -\frac{9}{5}x - 9 + 11$ $y = -\frac{9}{5}x + 2$

Final Equation:

The equation of the line is: $y = -\frac{9}{5}x + 2$

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Here are five related questions:

1. How do you convert a line equation from point-slope form to slope-intercept form?
2. What is the general form of a linear equation?
3. How can you find the slope if the points involve fractions?
4. How would the equation change if one of the points were on the y-axis?
5. What is the significance of the slope being negative?

Tip: If the slope is negative, it means the line is decreasing (sloping downwards) as you move from left to right.