Final answer:
To find the equation of the line that is perpendicular to y = -3x² and passes through the point (3, -1), we use the negative reciprocal of the original slope and the point-slope form of a linear equation to derive the equation y = 1/6x - 9/6.
Step-by-step explanation:
To find the equation of the line that is perpendicular to y = -3x² and passes through the point (3, -1), we need to first determine the slope of the original equation. The slope of y = -3x² is -6x, so the slope of the perpendicular line is the negative reciprocal of -6x. The negative reciprocal of -6x is 1/6x.
Using the point-slope form of a linear equation, y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope, we can substitute the values (3, -1) and 1/6x to get the equation of the line:
y - (-1) = 1/6x - 3/6
y + 1 = 1/6x - 3/6
y = 1/6x - 3/6 - 6/6
y = 1/6x - 9/6
The equation of the line that passes through the point (3, -1) and is perpendicular to y = -3x² is y = 1/6x - 9/6.