Final answer:
To find an equation of a line parallel to y = -6x + 10 and passing through the point (2, -3), determine that the slope of the new line is also -6 and use point-slope form to get the equation y = -6x + 9.
Step-by-step explanation:
To write an equation of a line that is parallel to a given line and passes through a specific point (P), you must first understand that parallel lines have the same slope (m). In this example, the given line is y = -6x + 10, which means the slope (m) is -6. Since we want a line parallel to the given line, our new line will also have a slope of -6.
The point-slope form of a line is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Plugging in the slope (-6) and the given point P(2, -3), the equation becomes y - (-3) = -6(x - 2).
Simplifying the equation, we get y + 3 = -6x + 12. Subtract 3 from both sides to get the final equation of the line in slope-intercept form: y = -6x + 9.