To write the equation of a line passing through the points $(2, 7)$ and $(0, -5)$, we can use the point-slope form of a linear equation:

1. Find the Slope (m): The slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the points $(2, 7)$ and $(0, -5)$: $m = \frac{-5 - 7}{0 - 2} = \frac{-12}{-2} = 6$

2. Use Point-Slope Form: The equation of a line in point-slope form is: $y - y_1 = m(x - x_1)$ Using the point $(2, 7)$ and the slope $m = 6$: $y - 7 = 6(x - 2)$

3. Simplify to Slope-Intercept Form (y = mx + b): Expanding the equation: $y - 7 = 6x - 12$ Adding 7 to both sides: $y = 6x - 5$

So, the equation of the line is: $y = 6x - 5$

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Related Questions

1. How can you determine the equation of a line given its slope and a single point on it?
2. What is the general form of a linear equation, and how does it differ from slope-intercept form?
3. How would the equation change if one of the points were different?
4. What does the slope tell us about the direction and steepness of a line?
5. How do you find the x-intercept and y-intercept of a linear equation?

Tip

Always double-check the slope calculation, as a small error can affect the entire equation.